Calculus Answers

the equation for a projectile height versus time is h(t)= -16^2+ Vot+ho

a tennis ball machine serves a ball vertically into the air from a height of two feet, with an initial speed of 120 feet per second . after how many seconds does the ball attain its maximum height

A farmer has 800m of fencing material to be enclose a rectangular pen adjacent to a long-existing wall. He will use the wall for one side of the pen and the available fencing material for the remaining three sides. What is the maximum area that can be enclosed this way?

A commuter train carries 600 passengers each day from a town to a city. A one-way trip costs 100 per person. Market research reveals that 10 fewer people would ride the train with every 1 increase in the fare. What fare should be charged to get the largest possible revenue?

Let f(x)= (x^2-2x)/(x^2-4)

For the function above, please find the following:

a) The domain of the function

b) The real zeroes of the function

c) The limit as × approaches 2 of f(x).

d) Plot f(x)

A measure of how hot weather feels to an average person is the Apparent Temperature Index.

A model for this index is:

A = 0.885t − 22.4h + 1.20th − 0.544,

where A is the apparent temperature in degrees Celsius, t is the air temperature, and h is the

relative humidity in decimal form.

a) Find ∂A/∂t and ∂A/∂h when t = 300 and h = 0.80.

b) Which has a greater effect on A, air temperature or humidity? Explain.

Write down T3(x), T4(x), and T5(x) for the Taylor series of f(x) = ln (3 + 4x) about x = 0.

Graph all three of the Taylor polynomials and f(x) on the same graph for the interval [−1/2,2]using programming tool.

The function J1 defined by

J1(x) = ∑((((−1)^n).x^(2n+1))/(n! (n + 1)! 2)).2n+1

n=0

,

is called the Bessel function of order 1.

a) Find its domain.

b) Graph the first several partial sums on a common screen using programming software.

Construct a table of values to investigate the following limits.

1. lim (10/x-2)

x-> 7

2. lim (x+6/x+2)

x-> 1

3. lim f(x)

x-> -1

If f(x) { 1/x if x ≤ -1}

If f(x) { x2-2 if x > -1}

Find the center of mass of a triangular lamina with vertices (0,0),(1,0) and (0,2)

if the density function is ρ(x,y)=1+3x+3y