Calculus Answers

Solve the corresponding equation for the appropriate interval by using the following two root finding techniques :

a) algebraic approach

sin(x+ π /2)=ln|x-1|

The specific gravity of a liquid is 0.79 kg/m^3. Calculate

the mass density and the specific weight of the liquid.

All 77 rooms in a motel will be rented each night if the manager charges $40 or less per room. If he charges $(40+z) per room, then 2z rooms will remain vacant. If each rented room costs the manager $7 per day and each unrented room $2 per day in overhead, how much should the manager charge per room to maximise his profit?

A man 6 ft. tall walks away from a lamp post 18 ft. high at the rate of 4 ft. per second. How fast does

the shadow of the man lengthen?

A ladder 5 meters long is leaning against the wall. The bottom is initially 3.5 meters away from the

wall. You are pushing it towards the wall at a rate of 0.20 m/s. How fast is the top of the ladder moving

up the wall 12 seconds after you start pushing?

Find the area of the region that lies inside the circle r = 3sin"\\theta" and outside the cardioid r = 1+sin"\\theta"

If the domain of f

f is -3\le x \le 3

−3≤x≤3, what is the range

Determine the formula for the nth term of the sequence:

a) -2, 1, 7, 25, 79, ....

b) 0, 1, 3, 7, 15, ....

Examine the series for convergence for summation of ((-1)^(n-1) sin(nx))/n^3

A box is to be made out of a piece of cardboard 38 cm x 38 cm, by cutting equal squares out of the

corners and turning up the sides. Find the volume of the largest box that can be made.