Questions in Section Calculus I

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.

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole?

A plane flying horizontally at an altitude of 1 mi and a speed of 570 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 3 mi away from the station. (Round your answer to the nearest whole number.)

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 60 mm?

Find the critical points of the function `g(x)=sqrt(4-x^2)`.