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.)

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