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What is the difference between Taylor series and Maclaurin series?
A Maclaurin series is centered about zero, while a Taylor series is centered about any point c. M(x) = [f(0)/0!] + [f'(0)/1!]x +[f''(0)/2!](x^2) + [f'''(0)/3!](x^3) + . . . for f(x). T(x) = [f(c)/0!] + [f'(c)/1!](x-c) +[f''(c)/2!]((x-c)^2) + [f'''(c)/3!]((x-c)^3) + . . . for f(x).
What is a critical point?
Critical point (in one variable): A point on the graph y = f(x) at which f is differentiable and f'(x) = 0. The term is also used for the number c such that f'(c) = 0. The corresponding value f(c) is a critical value. A critical point c can be classified depending upon the behavior of fin the neighborhood of c, as one of following:1. a local minimum, if f'(x) > 0 to the left of c and f'(x)< 0 to the right of c.2. a local maximum, if f'(x) < 0 to the left of c and f'(x)> 0 to the right of c.3. neither local maximum nor local minimum:a) if f'(x) has the same sign to the left and to the right of c, in which case c is a horizontal point of inflection.b) if there is an interval at every point of which f'(x) = 0 and c is an endpoint or interior point of this interval.(This is called the first derivative test).The second derivative test (is also a test for maximum and minimum values. It is a consequence of the concavity test):Suppose f is continuous near c.1. If f'(c) = 0 and f''(c) > 0, then f has a local minimum at c.2. If f'(c) = 0 and f''(c) < 0, then f has a local maximum at c.Example: f(x) = x^3 - 12x + 1(a) Find the intervals on which f is increasing or decreasing.(b) Find the local maximum and minimum values of f.(c) Find the intervals of concavity and the inflection points.Solution:(a) f(x) = x^3 - 12x + 1f'(x) = 3x^2 - 12f'(x) = 3(x +2)(x - 2)Interval: x < -2; -2 x < 2; x > 2x + 2: - ; +; +x - 2: - ; - ; +f'(x): + ; - ; +f: increasing on (-∞, -2); decreasing on (-2, 2); increasing on (2, ∞) So f is increasing on (-∞, -2) and (2, ∞) and f is decreasing on (-2, 2).(b) f changes from increasing to decreasing at x = -2 and from decreasing to increasing at x = 2. Thus f(-2) = 17 is a local maximum value and f(2) = -15 is a local minimum value.(c) f''(x) = 6xf''(x) > 0 ↔ x > 0 and f''(x) < 0 ↔ x < 0. Thus f is concave upward on (0, ∞) and concave downward on (-∞, 0). There is an inflection point where the concavity changes, at (0, f(0)) = (0, 1).
Which of his measurements is the most accurately A 213 degrees F B 211.1 degrees F C 212.89 degrees F D 211.8 degrees F?
C C is to 2 decimal places.
What is f(2) if f(x) (x 1)2?
it was C for anyone who comes across this question…
What is 350 degrees F in degree c?
350°F → (350 - 32) × 5/9 °C = 176 2/3 °C ≈ 176.67°C For cooking purposes, 350°F (Gas Mark 4) is converted at 175°C
What is the difference between Taylor series and Maclaurin series?
A Maclaurin series is centered about zero, while a Taylor series is centered about any point c. M(x) = [f(0)/0!] + [f'(0)/1!]x +[f''(0)/2!](x^2) + [f'''(0)/3!](x^3) + . . . for f(x). T(x) = [f(c)/0!] + [f'(c)/1!](x-c) +[f''(c)/2!]((x-c)^2) + [f'''(c)/3!]((x-c)^3) + . . . for f(x).
Is -2 degrees in Celsius or Fahrenheit?
Could be either. -2 C = 28.4 F -2 F = -18.89 C
What are the notes for moztart melody to play on the flute?
Bb Bb F F G G F (hold for 2 beats) Eb Eb D D C C Bb (hold for 2 beats) F F Eb Eb D D C (hold for 2 beats) F F Eb Eb D D C (hold for 2 beats) Bb Bb F F G G F (hold for 2 beats) Eb Eb D D C C Bb (hold for 2 beats)
The blues is based on a 12-bar chord progression Describe the progression?
In C its C C C C F F C C G F C C u can transpose 2 any key
What are the Notes for who can it be now alto sax?
Alto sax: Intro/Chorus: Bb f f# c#... f# f x 4 (2:04) C#, C#, C# C# e, e f# e e, e C# C# C#, C# Bb, Ab, F, Eb, F, Ab, Bb, C# C# e ab ab f# f.. f# f C# e f# ab, ab ab bb b bb b bb ab f# ab... f# e eb C# B Ab F# Ab Bb Ab, Bb, C#. C# e., C# C# C# e e C#, e, f# e f# e C# e ab c#.... Outro: f#, f, Bb
What are the musical notes to play empire state of mind on keyboard?
T| Capitals on the notes signify sharps (the black keys) A| B| Also see my Alicia Keys tab of the Empire State of Mind 2 for the chords! N| PEACE! A| ~Steph~ B| B| E| R5|F-F-F----- R| R4|F-F-F----- .| L3|F-F-F-F--- C| L3|----C----- O| L2|b-b---F--- M| -| R6|F-F-F---F---F---F-F-F--- T| R6|C-C-C---C---C---C-C-C--- A| R5|A-A-A---A---A---A-A-A--- B| N| L3|F-f----- A| L3|C-C----- B| L2|----b--- B| L2|----F--- E| L1|----b--- R| .| R6|F-F-F---F---F---F-F-F--- C| R6|C-C-C---C---C---C-C-C--- O| R5|A-A-A---A---A---A-A-A--- M| -| L3|F-F-F--- T| L3|--C----- A| L2|b---F--- B| N| R6|F-F-F---F---F---F-F-F--- A| R6|C-C-C---C---C---C-C-C--- B| R5|A-A-A---A---A---A-A-A--- B| E| L3|F-f----- R| L3|C-C----- .| L2|----b--- C| L2|----F--- O| L1|----b---
What are the piano chords to nicest thing by Kate Nash?
T| 3|-d-f-d-f-d-f-c-f-c-f-c-f----f----f----f-a-f-a-f-a------------------| A| 2|-------------------------A----A----A--------------------------------------| B| and then again with d and so on ...
What is a critical point?
Critical point (in one variable): A point on the graph y = f(x) at which f is differentiable and f'(x) = 0. The term is also used for the number c such that f'(c) = 0. The corresponding value f(c) is a critical value. A critical point c can be classified depending upon the behavior of fin the neighborhood of c, as one of following:1. a local minimum, if f'(x) > 0 to the left of c and f'(x)< 0 to the right of c.2. a local maximum, if f'(x) < 0 to the left of c and f'(x)> 0 to the right of c.3. neither local maximum nor local minimum:a) if f'(x) has the same sign to the left and to the right of c, in which case c is a horizontal point of inflection.b) if there is an interval at every point of which f'(x) = 0 and c is an endpoint or interior point of this interval.(This is called the first derivative test).The second derivative test (is also a test for maximum and minimum values. It is a consequence of the concavity test):Suppose f is continuous near c.1. If f'(c) = 0 and f''(c) > 0, then f has a local minimum at c.2. If f'(c) = 0 and f''(c) < 0, then f has a local maximum at c.Example: f(x) = x^3 - 12x + 1(a) Find the intervals on which f is increasing or decreasing.(b) Find the local maximum and minimum values of f.(c) Find the intervals of concavity and the inflection points.Solution:(a) f(x) = x^3 - 12x + 1f'(x) = 3x^2 - 12f'(x) = 3(x +2)(x - 2)Interval: x < -2; -2 x < 2; x > 2x + 2: - ; +; +x - 2: - ; - ; +f'(x): + ; - ; +f: increasing on (-∞, -2); decreasing on (-2, 2); increasing on (2, ∞) So f is increasing on (-∞, -2) and (2, ∞) and f is decreasing on (-2, 2).(b) f changes from increasing to decreasing at x = -2 and from decreasing to increasing at x = 2. Thus f(-2) = 17 is a local maximum value and f(2) = -15 is a local minimum value.(c) f''(x) = 6xf''(x) > 0 ↔ x > 0 and f''(x) < 0 ↔ x < 0. Thus f is concave upward on (0, ∞) and concave downward on (-∞, 0). There is an inflection point where the concavity changes, at (0, f(0)) = (0, 1).
What are the piano notes for mad world?
Gary Jules version: (based off a tab by slippy) Acoustic Grand Piano. 5|---c--------------------|-----------------------| 4|G--g--g--G--f--g--D--d--|------f-----------f--G-| 4|------c--g-----f--c-----|------d-----------d----| 3|f-----G-----f-----G-----|A-----------A----------| 5|---c--------------------|------------------------|------------------------| 4|---g--g--G--f--g--G--A--|------f-----------f-----|------f--f--G--G--f--f--| 4|------c--g-----f--c--f--|------d-----------d-----|------c-----------c-----| 3|f-----G-----f-----G-----|A-----------A-----------|f-----G-----f-----G-----| 5|c--c-----c-------------|-----------------------| 4|------D--------G--D----|A--A-----A-----g-------| 4|------c-----------c----|-----------------------| 3|G-----------G----------|D-----g-----D-----A----| 3|-----------------------|------A-----------g----| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------c-----| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----G-----| 5|c--c-----c-------------|-----------------------| 4|------D--------G--D----|A--A-----A-----g-------| 4|------c-----------c----|-----------------------| 3|G-----------G----------|D-----g-----D-----A----| 3|-----------------------|------A-----------g----| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------c-----| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----G-----| 5|c--c-----c-------------|-----------------------| 4|------D--------G--D----|A--A-----A-----g-------| 4|------c-----------c----|-----------------------| 3|G-----------G----------|D-----g-----D-----A----| 3|-----------------------|------A-----------g----| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------c-----| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----G-----| 5|c--c-----c-------------|-----------------------|----------------------| 4|------D--------G--D----|A--A-----A-----g-------|A--A----A----G--g--f--| 4|------c-----------c----|-----------------------|f---------------------| 4|-----------------------|-----------------------|d---------------------| 3|G-----------G----------|D-----g-----D-----A----|A---------------------| 3|-----------------------|------A-----------g----|----------------------| 5|-----------------c---c---|d---------------d---d----------| 4|G----f--f--G--G--G---G---|f---A---f---A---f---f---A---A--| 4|f----c-----f--f--f---f---|----f---d---f-----------f---f--| 4|-----------------c-------|------------------------f------| 4|-------------------------|------------------------d------| 3|f----G-----f-----G-------|A---------------A--------------| 5|------------------c---c---|d--------------d---d----------| 4|G-----f--f--G--G--G---G---|f---A---A---A--f---f---A---A--| 4|f-----c-----f--f--f---f---|----f---f---f----------f---f--| 4|------------------c-------|--------f--------------f------| 4|--------------------------|--------d--------------d------| 3|f-----G-----f-----G-------|A--------------A--------------| 5|------------------c---c---|d---------------d---d----------| 4|G-----f--f--G--G--G---G---|f---A---f---A---f---f---A---A--| 4|f-----c-----f--f--f---f---|----f---d---f-----------f---f--| 4|------------------c-------|------------------------f------| 4|--------------------------|------------------------d------| 3|f-----G-----f-----G-------|A---------------A--------------| 5|------------------c---c---|d---------------d---d-----------| 4|G-----f--f--G--G--G---G---|f---A---A---A---f---f---A---A---| 4|f-----c-----f--f--f---f---|f---f---f---f-----------f---f---| 4|------------------c-------|d-------------------------------| 3|f-----G-----f-----G-------|A-------------------------------| 5|---c-----------------------|---------------------| 4|G--g--g--G---G---g---D--d--|f----f---------f--G--| 4|------c--g---f---f---c-----|-----d---------d-----| 3|f-----G------f-------G-----|A---------A----------| 5|---c-------------------------|--------------------| 4|---g--g--G---G---g---G---A---|-----f---------f----| 4|------c--g---f---f---c---f---|-----d---------d----| 3|f-----G------f-------G-------|A---------A---------| 5|-----------------------|c--c-----c--------------|-----------------------| 4|-----f--f--G--G--f--f--|------D--------G--D-----|A--A-----A-----g-------| 4|-----c-----------------|------c-----------c-----|-----------------------| 3|f----G-----f-----------|G-----------G-----------|D-----A-----D-----A----| 3|-----------------------|------------c-----------|------g-----------g----| 2|f----------------f-----|G-----------------------|-----------------------| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------------| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----------| 3|d-------------------------|-----------------------| 2|--------------------------|f----------------f-----| 5|c--c-----c--------------|-----------------------| 4|------D--------G--D-----|A--A-----A-----g-------| 4|------c-----------c-----|-----------------------| 3|G-----------G-----------|D-----A-----D-----A----| 3|------------c-----------|------g-----------g----| 2|G-----------------------|-----------------------| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------------| 4|------------------d-------|-----------------------| 3|d-------------------------|-----------------------| 2|--------------------------|f----------------g-----| 5|c--c-----c--------------|-----------------------| 4|------D--------G--D-----|A--A-----A-----g-------| 4|------c-----------c-----|-----------------------| 3|G-----------G-----------|D-----A-----D-----A----| 3|------------c-----------|------g-----------g----| 2|G-----------------------|-----------------------| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------------| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----------| 3|d-------------------------|-----------------------| 2|--------------------------|f----------------f-----| 5|c--c-----c--------------|-----------------------|----------------------| 4|------D--------G--D-----|A--A-----A-----g-------|A--A----A----G--g--f--| 4|------c-----------c-----|-----------------------|f---------------------| 4|------------------------|-----------------------|d---------------------| 3|G-----------G-----------|D-----A-----D-----A----|A---------------------| 3|------------c-----------|------g-----------g----|----------------------| 2|G-----------------------|-----------------------|----------------------| 5|-----------------c---c---|d------------d---d----------| 4|G----f--f--G--G--G---G---|f---A--f--A--f---f---A---A--| 4|f----c-----f--f--f---f---|----f--d--f----------f---f--| 4|-----------------c-------|---------------------f------| 4|-------------------------|---------------------d------| 3|f----G-----f-----G-------|A------------A--------------| 2|f------------------------|A---------------------------| 5|-----------------c---c---|d-------------d---d----------| 4|G----f--f--G--G--G---G---|f---A--A---A--f---f---A---A--| 4|f----c-----f--f--f---f---|----f--f---f----------f---f--| 4|-----------------c-------|-------f--------------f------| 4|-------------------------|-------d--------------d------| 3|f----G-----f-----G-------|A-------------A--------------| 2|f------------------------|A----------------------------| 5|-----------------c---c---|d------------d---d----------| 4|G----f--f--G--G--G---G---|f---A--f--A--f---f---A---A--| 4|f----c-----f--f--f---f---|----f--d--f----------f---f--| 4|-----------------c-------|---------------------f------| 4|-------------------------|---------------------d------| 3|f----G-----f-----G-------|A------------A--------------| 2|f------------------------|A---------------------------| 5|-----------------c---c---|d---------------d---d-----------| 4|G----f--f--G--G--G---G---|f---A---A---A---f---f---A---A---| 4|f----c-----f--f--f---f---|f---f---f---f-----------f---f---| 4|-----------------c-------|d-------------------------------| 3|f----G-----f-----G-------|A-------------------------------| 2|f------------------------|--------------------------------| 5|---c-----------------------|---------------------| 4|G--g--g--G---G---g---D--d--|f----f---------f--G--| 4|------c--g---f---f---c-----|-----d---------d-----| 3|f-----G------f-------G-----|A---------A----------| 5|---c-------------------------|--------------------| 4|---g--g--G---G---g---G---A---|-----f---------f----| 4|------c--g---f---f---c---f---|-----d---------d----| 3|f-----G------f-------G-------|A---------A---------| 5|---c-----------------------|--------------------| 4|G--g--g--G---G---g---D--d--|f----f---------f----| 4|------c--g---f---f---c-----|-----d---------d----| 3|f-----G------f-------G-----|A---------A---------| 4|G--G--g---g---f---f---D---d--|----------------- 4|------c---------------c------|----------------- 3|f-----G-------f-------G------|A---------------- 3|-----------------------------|f---------------- 2|-----------------------------|A---------------- < I found this very helpful and many thank you both slippy and Katie for all their hardwork!> Sungod357 Gary jules: Mad world Beginning: G# up to C down to G up to G# down to F up to G down to D# down to D down to A# up to D down to A# up to D (2 times) G# up to C down to G up to G# down to F up to G up to G# up to A# down to A# up to D down to A# up to D --------------------------------------------------------- a more advanced version with chords and stuff: On the left hand play the "G# up to C down to G up to G# down to F up to G down to D# down to D" bit except instead of "down to A# up to D down to A# up to D", Do A# then D and F at the same time. Meanwhile, your right hand plays this chord F and then G# and C Okay mad. Try this now. F F G# G# F F C C C G# A# A# A# G A# A# A# G# G F repeat it a few times
Can anyone give you the flute chords of moon river?
The Sequence is as follows: G D2 C2 / B A G F G / C B A G F G / C D / E C G E / D C G E / D C E G C2 B / A B A G A / C ... G D2 C2 / B A G F G / C B A G F G / C D / E C E G C2 D2 C2 G / B A G F G / C B A G F C / C E D E C / (Repeat 2x Then End). or The Sequence for the Higher Sound Ver. Of Moon River A E2 D2 / C#2 B A G A / D C#2 B A G A / D E / F# D A F# / E D A F# / E D F# A D2 C#2/ B C#2 B A B / D ... A E2 D2/ C#2 B A G A / D C#2 B A G A / D E / F# D F# A D2 E2 D2 A / C#2 B A G A / D C#2 B A G D / D F# E F# D / (Repeat 2x Then End).
What is the lyre chords of superbass?
c# d# f# g# a# g# f# f# f# f# f# d# c# d# f# g# a# g# f# f# f# f# f# d# f f f f f f f d# c# c# c# d# d# d# c# f f f f f f f d# c# c# c# d# d# d# c# a# a# c# d# a# a# c# d# f f f f f f f d# c# c# c# d# d# d# c# f f f f f f f d# c# c# c# d# d# d# c#
What is the superbass lyre chords?
c# d# f# g# a# g# f# f# f# f# f# d# c# d# f# g# a# g# f# f# f# f# f# d# f f f f f f f d# c# c# c# d# d# d# c# f f f f f f f d# c# c# c# d# d# d# c# a# a# c# d# a# a# c# d# f f f f f f f d# c# c# c# d# d# d# c# f f f f f f f d# c# c# c# d# d# d# c#
