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).
The conversion equation is F = (9/5)C + 32. To convert 0 deg. C to F, replace C with 0, and the answer is 32 deg. F, or the freezing point of water.
32 degrees Fahrenheit is equal to 0 degrees Celsius.
type "0 f to c" in google search it is -17.7777778 degrees Celsius
32°f = 0 °c
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0°F = -17.8°C(0°F - 32) multiplied by 5/9 = -17.8°C
0°C = 32°F 0°F = -17.8°C (about the same temperature as a home freezer)
Calculate the midpoint � = � � 2 c= 2 a+b . Evaluate � ( � ) f(c). Determine the sign of � ( � ) f(c). If � ( � ) = 0 f(c)=0, you've found the root. If � ( � ) f(c) has the same sign as � ( � ) f(a), set � = � a=c. If � ( � ) f(c) has the same sign as � ( � ) f(b), set � = � b=c
0 K is equal to -459.67 °F The theoretical temperature "absolute zero" is 0 K, -273.15 °C, or -459.67 °F. 0°K = -459.67°F = -273.15 °C
0oF is colder
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).