Calculus Answers

Find the derivative of f(x) = 5 divided by x at x = -1.

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.)
f(t) = 9 cos t, −3π/2 ≤ t ≤ 3π/2

Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 5 as x approaches 5 from the left.

A geometric series has first term a and common ratio r where a and r are positive constants.The fourth term of the series is 1/p , the sum to infinity of the series is p and the sum of the first two terms of the series is 0.75p where p is a positive constant.
Find the values of a,r and p.

The function t(x) at the point T(3,18) has gradient 1.5*t(x) . Given the second derivative of the function t(x) is 2(3x +1) , sketch the curve of y=t(x) clearly showing any points of intersection with the coordinate axes.

state and prove second mean value theorem for integrals

find the fourier series for the periodic function f(x) with the period 2 π given by
f(x)=2x, - π< x< π

Intergrate the following expressions
(integral) (2x^3-3x^2+5x-2)dx
(integral) (5sin2+2cos4)d

Force needed to compress spring is given by
F=kx
Where K is the spring constant= 10N/cm
F is the force/N
x=distance compressed/cm
Use intergration to find the work done on the spring as it is compressed between x=1 and x=3cm.

Calculate dy/dx and d^2y/dx^2 for the following parametric equations:
y=t^2 e^-t^2
x=tan(t)