# Questions in Section Calculus I: page 3

Find the polar coordinates of the point P whose rectangular coordinates are (-2, -2sqrt(3)).

Find the leftmost point on the upper half of the Cardioid r=1+cos(phi).

What is the sum of the Maclaurin series pi-pi^3/(3!)+pi^5/(5!)+...+(-1)^n*(pi^(2n+1))/((2n+1)!)+... ?

Differentiate the function y=(e^(9u)-e^(-9u))/(e^(9u)+e^(-9u)).

There are two poles that are 200m apart. A wire is spread across to make a catenary. Each post is 100m tall and the wire is 50m above the ground at the lowest point. Knowing the equation y(x)=a*cosh(x/a)+b, what values must a and b be in order to fit the constraints? What is the length of the cable?

Find the amplitude and period, and sketch at least two periods of the following function: y=1/2cos(3x-pi).

Find following limits:

1. lim_(x->oo)(1-e^x)/(1+e^x)
2. lim_(x->0) (sqrt(x+4)-2)/(x)

Sketch the graph of y=(x-1)/x by translating, relecting, compressing and stretching the graph of y = 1/x.

What is the largest domain for which y=3sin((2x)/3) is invertible? Find the inverse function on this domain.

Define a continuous function which is differentiable everywhere except at x=-1/2, and formally justify that it is continuous but not differentiable there.