Calculus — popular questions

Are one-to-one functions either always increasing or always decreasing

OABC is a parallelogram and M is the midpoint of BC

Prove that the bodies do not meet

Show that the distance between the bodies after t seconds

Small bodies P and Q are moving with constant velocities

What is the area of the region enclosed by the graphs of $y=e^x-2$, $y=\sin x$, and $x=0$ ?

To help restore a beach, sand is being added to the beach at a rate of $s(t)=65+24\sin(0.3t)$

The base of a solid is the region enclosed by the curve $\frac{x^4}{16}+\frac{y^4}{81}=1$

Consider the differential equation dy/dx=3(x-2)(y-3) where y<0

Consider the differential equation dy/dx=2x/y