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Evaluate Limit x tends to 0 x minus sinx divided by tanx minus x?
lim (x→0) [(x - sin x)/(tan x - x)]Since both the numerator and the denominator have limit zero as x tends to 0, the quotient is indeterminate at 0 and of the form 0/0. Therefore, we apply the l'Hopital's Rule and the limit equalslim (x→0) [(x - sin x)'/(tan x - x)']= lim (x→0) [(1 - cos x)/(sec2 x - 1)] (form 0/0, use again the l'Hopital's Rule)= lim (x→0) [(1 - cos x)'/(sec2 x - 1)']= lim (x→0) [(0 - (-sin x)/(2sec x sec x tan x - 0)]= lim (x→0) [(sin x)/(2sec2 x tan x)] (substitute 1/cos2 x for sec2 x and sin x/cos x for tan x)= lim (x→0) [(sin x)/(2sin x/cos3 x)]= lim (x→0) [(sin x cos3 x)/2sin x]= lim (x→0) (cos3 x/2)= 1/2Thus, (x - sin x)/(tan x - x) tends to 0.5 as x tends to 0.
Integration of sinx is?
-cos x + C
What is the indefinite integral of 2 over X?
S 2/x d/x bring the constant 2 out in front of the sign of integration 2 S 1/x dx you should know the integration of 1/x 2*ln(x) + C
What is integration of x to the power x with respect to x?
Apparently that can't be solved with a finite number of so-called "elementary functions". You can get the beginning of the series expansion here: http://www.wolframalpha.com/input/?i=integrate+x^x
Integral of sinx cosx sin2x cos3x dx?
Integral[sin(x)cos(x)sin2(x)cos3(x)] dxgather termsintegral[sin3(x) cos4(x)] dxpull one sin(x) as sin is oddintegral[sin2(x) cos4(x) sin(x)] dxusing trig identitiesintegral[(1 - cos2(X)) cos4(x) sin(X)] dxu substitutionu = cos(x)du = - sin(x) dxsointegral[(1 - u2)) (u4) - du] dx- integral[(1- u2)) u4 du] dx= u - 1/3u3 + 1/5u5 du= cos(x) - 1/3cos3(x) + 1/5cos5(x) + C============================
Integration cos3 x?
Take f(x) = cos(3x) ∫ f(x) dx = ∫ cos(3x) dx Take u=3x → du = 3dx = ∫ 1/3*cos(u) du = 1/3*∫ cos(u) du = 1/3*sin(u) + C, C ∈ ℝ = 1/3*sin(3x) + C
Solution of Double integration 13.1 calculus by thomos finney?
x integration 0 x integration x siny/ydydx
Integration of square of tangent inverse x?
Integration for inverse tangent of square x
Cos x - cos x sin2 x equals cos3x?
cos(x)-cos(x)sin2(x)=[cos(x)][1-sin2(x)]cos(x)-cos(x)sin2(x)=[cos(x)][cos2(x)]cos(x)-cos(x)sin2(x)=cos3(x)
What is the integration of sinehx?
It is cosh(x) + c where c is a constant of integration.
What is integration of 34?
Assuming integration is with respect to a variable, x, the answer is 34x + c where c is the constant of integration.
Integration of sin x?
Integration by Parts is a special method of integration that is often useful when two functions.
Integration of x2 x 12?
_____ 1 x (x+4) (x-3)
Evaluate Limit x tends to 0 x minus sinx divided by tanx minus x?
lim (x→0) [(x - sin x)/(tan x - x)]Since both the numerator and the denominator have limit zero as x tends to 0, the quotient is indeterminate at 0 and of the form 0/0. Therefore, we apply the l'Hopital's Rule and the limit equalslim (x→0) [(x - sin x)'/(tan x - x)']= lim (x→0) [(1 - cos x)/(sec2 x - 1)] (form 0/0, use again the l'Hopital's Rule)= lim (x→0) [(1 - cos x)'/(sec2 x - 1)']= lim (x→0) [(0 - (-sin x)/(2sec x sec x tan x - 0)]= lim (x→0) [(sin x)/(2sec2 x tan x)] (substitute 1/cos2 x for sec2 x and sin x/cos x for tan x)= lim (x→0) [(sin x)/(2sin x/cos3 x)]= lim (x→0) [(sin x cos3 x)/2sin x]= lim (x→0) (cos3 x/2)= 1/2Thus, (x - sin x)/(tan x - x) tends to 0.5 as x tends to 0.
Integration of root x?
(2/3)x^(3/2)
Integration of sinx is?
-cos x + C
Integration Read 1st answer for more info?
What is the [int] (x+1)*5^[(x+1)^2]? [int]= integration I got 5^[(x+1)^2]/ 2ln 5. Is this correct?
