# 8 Calculus Questions to Answer Detailed

**Question description**

1) Improper Integrals

integral from 1 to infinity of 3/(x^4)dx

2) Improper Integrals

integral from -infinity to infinity of x^3(1+x^4)^-2 dx

3) Find the volume of the solid of revolution obtained by revolving the region bounded by the graphs of the functions about the x-axis

y=1/2x+3 and y=x^2

4) Find the volume of the solid of revolution obtained by revolving the region bounded by the graphs of the functions about the x-axis

y=1/x, y=x and y=2x

5) Taylor polynomial

f(x)=ln(x) at x=1, n=4

6) Taylor Polynomial

1/(2x+3) at x=0, n=3

7) Taylor Polynomial

f(x)=e^(2x) at x=1, n=4

8) Find the 3rd Taylor Polynomial of f(x)=e^(-x/2) at x=0 and use it to estimate e^(-0.1)

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