Questions in Section Calculus I: page 2

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)`.

Find `cos(arcsin(x))`.

How do we calculate the second derivative of the following implicitly define equation: `x^2+y^2=90^2`?

Find the derivative of the function using the definition of derivative: `f(t)=5t-2t^2`.

What is range of `csc(x)`?

A particle moves along the circle `x^2+y^2=25`. If `x` increases at a rate of `2` units per minute, at what rate is `y` changing when `x=3`.

How the continuity and one-sided continuity related?

Is it true or false?

A curve in polar coordinates is symmetric about the origin if replacing `theta` by `pi+theta`, or replacing `r` by `-r` in its equation produces an equivalent equation.

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