# Questions in Section Calculus I

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.

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.)