Question 5 f(x) = esin x Find f'(x). -CO5xesinx 0 -sinx + sinx 0 sinxeỐsinx cosxesinx
sinx 5. (10 marks) Check whether f (x) = if x = 0 if x = 0 is differentiable at x-0. Prove it using an e- 8 proof. sinx 5. (10 marks) Check whether f (x) = if x = 0 if x = 0 is differentiable at x-0. Prove it using an e- 8 proof.
sinx 5. (10 marks) Check whether f(x) = if x 70 if x = 0 is differentiable at x=0. Prove it using an e-8 proof.
Check whether f(x)= sinx/x if x≠0 and f(x) = 1 if x=0 is differentiable at x=0. Prove it using an ε-δ proof.
Find the absolute maximum value and the absolute minimum value of the function f(x) = esin(x) on the interval [0,21]. Express the answer in terms of the natural number, e. Do not use decimal approximations of the answer. absolute maximum: absolute minimum:
-a" (a) Find the Taylor series for sinx about x 0, and prove that it converges to sinx uniformly on any bounded interval [-N,N (b) Find the Taylor expansion of sinx about xt/6. Hence show how to annrmximate D.
-a" (a) Find the Taylor series for sinx about x 0, and prove that it converges to sinx uniformly on any bounded interval [-N,N (b) Find the Taylor expansion of sinx about xt/6. Hence show how to annrmximate D.
Question 17 Find the derivative of the function f(x) = 4e*cosx . Simplify your answer. 0 a. 4e*(cosx-sinx) 0 b. 4e*(cosx + sinx) 0 C. 4e*cosx ( d. 4e*sinxcosx e. -4e* sinx A Moving to another question will save this response.
(10 marks) Check whether f(x) = sinx x if x0 if x = 0 is differentiable at *-0. Prove it using an e-8 proof.
Find F(x) for the following function. f(x)=-4x+2 Then find F(5), f(0) and f(-7). f(x)=___ f(5)=___ f(0)=___ f(-7)=___ Question complete.
QUESTION 17 Find the integral. - sin x cos xdx - sinox +C 6 - sinx 5 + sin 5x 5 +C sinx -C
3. Find the average value of the function f(x) = sinx on the interval [0,1].