Questions in Section Calculus I

Find `f(g(x))` if `f(x)=1/x` and `g(x)=(4-x)/(2+x)`

Find the equation of the tangent line to the graph `x^2+y^2-3xy=-11x` at the point `(-1,2)`.

1. Find the differential `dy` for `y=6tan(x)`
2. Evaluate `dy` for the given values of `x` and `dx`: `x=pi/3`, `dx=-0.1`

Let `f(x)=ax^2+bx+c`. Find `a`, `b`, `c` so that the tangent to the graph of `y=f(x)` at `(1,5)` has a slope of `1` and `f(0)=-5`.

Find the critical numbers of `f(x)=10x^2+6x`

Find `lim_(x->0)(ln(x))^tan(x)`.

Find the derivative of `y=(x^2+2/x^2+3)^(1/9)`

Find a polynomial `f(x)` of degree 3 that has the following zeros: 8, 0, -3.

A powerful earthquake had a magnitude of 8.2 on the Richter scale. An earthquake several years earlier was 1.44 times as intense. What was the magnitude of the earlier earthquake?

`lim_(x->oo)` `4^x/(x!)`

Use the squeeze theorem to find the answer.