Note that fe-*x dx = n! If X ~ Exp(X), then we can compute moments of X by using the above improper integral E[X] = { . E[X²] = E[X³] = %. Generally, the nth moment is E[X"]= Here, a= C = d=

Q: Suppose f"(x) = - (sin(x)), ƒ'(0) = –2, and f(0) = -3. %3D Find f(1/4).

A: Given,          Suppose f''x=-sinx , f'0=-2 and f0=-3.

Q: Find the first derivative of the following functions with respect to x: a) y= Inx3 b) y = ln (÷) c)…

A: We can make it easier for you.

Q: Let h(x) = f(x) = g(x). If f(x) = 9x² and g(x) = 8x, what is h'(-5)? - Do not include "h' (-5) =" in…

A: SOLUTION-

Q: 1 ["Co 0 Approximate e cos x dx using 0 P₂(x) dx OA. 1.75 OB. 1.25 O c. 1.125 O D. 1.5

A: Sol:- First find P2xA Maclaurin series is given byf(x)=∑k=0∞f(k)(a)k!xkIn our case,…

Q: Find y= tan' ( ) Sin Sa ® y= Sin" (x) ® y= log, [tanx]

A: We use the following methods to calculate differentiate d/dx of tan inverse x =1/1+x²  d/dx of sin…

Q: Suppose f(3) = 6 and f '(3) = 7. Find an equation of the tangent line to H(x) at x=3. %3D H(x) =…

A: We have,  Hx=x4-7fx, f3=6 and f'3=7 Using the chain rule of differentiation, H'x=x4-7·f'x+fx·4x3…

Q: For f(x) = ln |sin x |. Find f’ (3pie/4)

A: Given, f(x) = ln |sin x |

Q: Given the table of values below, find h'(1) if h(x) = Xx 1 f(x) 1 g(x) (x) 2 f'(x) 3 g(x) -3 g'(x)…

A:

Q: If f(x) = ln(x + ln(x)), what is f'(1). Show all work.

A:

Q: Find f f(x) dx if 4 for a 4.

A: I=∫05fxdxif fxdx=4for x<4xfor x≥4

Q: 2. Let h'(2) = 8, h' (2) = 5, h(2) = 3, h″(4) = −—1,h'(4) 4 ª[₂x x.h"(x) dx. 3, h(4) 6. Find = =

A:

Q: d dx f(x) = ex, f(0) = 8.

A:

Q: Evaluate 2x+4 1. fx e**dx 2. SInx dx 3. J x2-2x 4.(a) (e* + 1)2 dx, (b) Sx³e2x dx.

A:

Q: Differentiate cos cos" Vi-x? y = ecos

A:

Q: Find the equation of the tangent to the graph xey +y-2x = In 2. %3D Evaluate the derivative of the…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: If f(x) = 2 sin(x) + In(4x), find f '(x). f'(x) =

A: Given f(x)=2 sin(x)+ln(x) We know that d/dx(sin(x))=Cos(x) d/dx(ln(x))=1/x d/dx(xn)=nxn-1

Q: Suppose f'(x) = sin(4x²). d f(5x)=[ dx d ƒ(2x5) dx

A:

Q: Find the anti-derivative of

A: Answer and explanation is given below

Q: If ƒ(x) = sin(e²x), find ƒ'(x). ƒ'(x) = ←

A: Given function                             f(x) = sine2x   We have to find f'(x)

Q: Find y' if y = e^x. cos x

A:

Q: Just part 1C y=12^x plz show all work and do not simplify

A:

Q: ssume that h(x) = 1.5 − x and f(x) = 2(1-1/x^2) where 1<=x<=1.5. Calculate E[h(x)]

A: It is given that: hx=1.5-xfx=21-1x2, 1≤x≤1.5