Calculus — popular questionsPage 4

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

(b) Determine the bearing the boat should steer from P to Q

Water in a large river estuary flows at a constant 5.3 km/h on a bearing 165°

Why can't I define $\Delta u=(g(x)+\Delta x)-g(x)$?

If f(x) = axe^{-x} is an “M-function” on the interval $(0,+\infty)$

Sum of the series $\frac{1}{1\cdot 2\cdot 3\cdot 4}+\frac{4}{3\cdot 4\cdot 5\cdot 6}+\cdots$

Evaluate the limit $\lim_{n\to\infty}\sum_{i=1}^{n} f(c_i)\,\Delta x_i$ for $f(x)=\sqrt{x}$

$$\frac{d}{dt}\int_a^b f(x,t)\,dx=\int_a^b \partial_t f(x,t)\,dx$$

The figure above shows the region A, which is bounded by the x- and y-axes, the graph of $f(x)=\frac{\sin x}{x}$

If $F(x)=\int_0^x f(t)\,dt$, and $F(a)=-2$ and $F(b)=-2$

Let $f(x)=\int_{-2}^{x^2-3x} e^{t^2}\,dt$