Calculus Answers

Verify Green’s theorem in the plane for $ (xy + Sy?)dx + 3xdy,

where c is the closed curve of the region bounded by y = x and y = x?.

What is the derivative of cos4x

A light on the ground at Lilys building is 30meters away from the building. Jade is 2 meters tall. She walks from the light to the building at 1 meters per second. How fast is the shadow of Jade on the building changing when she is 15 meters from the building.

The point

(π/6 , 1/2)

is on a curve and at any point on the curve, the slope of the tangent line is given by

−2 sin(2x)

. Find an equation of the curve.

f(x) =lin(x+linx)

Determine the derivatives of the following functions:

a.f(x)=In(x+Inx)

b.g(x)=In√x-1÷x^4+1

C.h(x)=√xe^x^2-x(x+1)^2/3

d.y(x)=(sinx)Inx

Determine the derivatives of the following inverse trigonometric functions:

a.f(x)=tan^-1√x

b.y(x)=In(x^2cot^-1x/√x-1)

c.g(x)=sin^-1(3x)+cos^-1(x/2)

d.h(x)=tan-1(x-√x^2+1)

Conside the function f(x)=x to the power 4-2xcube+2x-1

A. Find the critical points of f(x)

B. Determine the interval over which f(x) is increasing and the interval on which it is decreasing.

At any point of the path x=3cos⁡t,y=3sin⁡t,z=4t, what is the Normal vector

indicate the function of f(x) below in fourier series

"0,-1<x<0"

"f(x)=" {

"1,0<x<3"