Questions from General Calculus

Q: A bacteria population starts with 400 bacteria and grows at a rate

A bacteria population starts with 400 bacteria and grows at a rate of r(t) = (450.268)e1.12567t bacteria per hour. How many bacteria will there be after three hours?

Q: An object with weight W is dragged along a horizontal plane by

An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle  with the plane, then the magnitude of the force is F = µ...

Q: Find the limit. lim θ→0

Find the limit. lim θ→0 cos θ−1 ) sin θ

Q: (a) Sketch, by hand, the graph of the

(a) Sketch, by hand, the graph of the function f (x) − ex, paying particular attention to how the graph crosses the y-axis. What fact allows you to do this? (b) What types of functions are f (x) − ex...

Q: Differentiate the function. S(R) = 4πR2

Differentiate the function. S(R) = 4πR2

Q: Find constants A and B such that the function y = A

Find constants A and B such that the function y = A sin x + B cos x satisfies the differential equation y’’ + y’ - 2y = sin x.

Q: Differentiate the function. h(u) = Au3 +

Differentiate the function. h(u) = Au3 + Bu2 + Cu

Q: Differentiate the function. j(x) = x24 +

Differentiate the function. j(x) = x24 + e24

Q: Differentiate the function. k(r) = er +

Differentiate the function. k(r) = er + re

Q: Differentiate the function. G(q) = (1

Differentiate the function. G(q) = (1 + q-1)2