Questions in Section Calculus I

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.

Find the polar coordinates of the point P whose rectangular coordinates are (`-2`, `-2sqrt(3)`).

Find the leftmost point on the upper half of the Cardioid `r=1+cos(phi)`.