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.

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