For the following integrals, find the constants A, B, etc., and then evaluate the integrals. (a) ∫1/[x(x^2+ 1)dx   (b) ∫1/[x^2(x^2+ 1)dx   4. (a) Using the Problems 3a and 3b above as guides, find the constants for ∫1/[x^6(x^2+ 1) dx, and note that after finding the constants, the integral can be evaluated in a straightforward manner. (b) After doing part (a), hopefully you can see how to proceed with ∫1/x^n(x^2+ 1)dx, for any positive integer n   **Note: The problems were connected so treat this problem as multi-questioned and dock me however many questions you think are included please **  .

Q: find the diferential of the function when x = 2 and dx = 0.1 f(x) = x ln (x^3 + 2x - 4)

A: We will use the definition of differential.

Q: d^2y/dx^2 for y=2x^3-5/x^2

A:

Q: If y=x^9 -x^1/2, find (d^2y)/(dx^2)

A:

Q: Find f'(1) if f(x) = √√√x + )=√x+ +2

A: We are given,

Q: Find the derivative of the function. x3 - 5x2 - 2x f(x) =' f'(x) =

A:

Q: 3(x5 + x³) ez"+xª + 3(x6 +xª) +2 dx -2

A:

Q: Simplify d/dx(x^2 dy/dx)

A: To simplify the given expression.

Q: For each of the following y, find the d^2y/dx^2

A: We know, d/dx (xn)= nxn-1, for any real number n. d/dx(u(x)v(x))= v(x)*d/dx(u(x))+u(x)*d/dx(v(x))

Q: If f(x)= ∫ (top 16, bottom 9) (-x^(-1/2)+5) dx. Enter your answer as an exact fraction of necessary.

A:

Q: Iff(x) = 3 xe", find f'(0)

A: We find f'(x) using product rule

Q: For y=f(x)=3x^3 , x=3 , and (triangle)x = 0.03 find dy (two decimal places)

A:

Q: Find d/dx((x)(d/dx(x-x^2))

A:

Q: What is r′(x) if r(x)=70x^5/2^x?

A: rx=70x52xTo find r′(x)

Q: Find the derivative 3x (x4+ 1)5 dx d 3x (x4 + 1)5]- dx

A: To find the derivative of [3x·(x4 + 1)5]

Q: Which of the following is  F(x)+C  for  F(x)=∫f(x)dx=∫(3e^x+2sin⁡x)dx  and  F(0)=0  ? Select one…

A:

Q: ∫sin(1/x8)dx/x9

A: We have to evaluate the integral: ∫  sin1x8dxx9 This integral will be solved by substitution method…

Q: ∫(x+9)dx/x^2−x−2

A: x+9x2-x-2=x+9x2-2x+x-2=x+9(x-2)(x+1)using partial fraction methodx+9(x-2)(x+1)=Ax-2+Bx+1at x=2  ,…