Calculus Answers

the diagram shows part of the curve y=2-18/(2x+3), which crosses the x-axis at A and the y-axis at B.The normal to the curve at A crosses the y-axis at C.The normal to the curve at A crosses the y-axis at C.find the length of BC

∫▒1/(x-√(x+2)) dx

Simplify:

(1/3)((2x^2)^(-2/3)) * (4x) + (1/2)((3x)^(-3/2)) * (3)

Suppose that for a company manufacturing calculators, the cost, and revenue equations are given by C=70000+40x, R=400−x220, where the production output in one week is x calculators. If the production rate is increasing at a rate of 500 calculators when the production output is 6000 calculators, find each of the following:

Use the unit circle to give a convincing argument for the identity.
(a) sin (t+pi) = -sin t
(b) cos (t+pi) = -cos t

A hot-air balloon over Albuquerque, New Mexico, is being blown due east from point P and traveling at a constant height of 800 ft. The angle y is formed by the ground and the line of vision from P to the balloon. This angle changes as the balloon travels.
(a) Express the horizontal distance x as a function of the angle y.
(b) When the angle is pi over 20 rad, what is its horizontal distance from P?
(c) An angle of pi over 20 rad is equivalent to how many degrees?

What is the integaral of (y+4)dy over y+16?

simplify: (3^(x+1) - 3x) / [2(3^x) - 3^(x-1)]

du/dt of (t^-.5)e^(((-x^2)/((4k^2)t))
Also d2u/dx2

Find the average value of the function over the given interval and every (all) value(s) of in the interval for which the function equals its average value.

f (x) = [4(x^2)+1]/x^2
over the interval [1,3]