Calculus Answers

Solve the following differential equation
(D-1)^2(D^2+1)^2y=sin^2(x/2)+e^x+x

The price P per unit at which a company can sell all that it produces is given by the function P(x) = 300 — 4x. The cost function is
c(x) = 500 + 28x where x is the number of units produced. Find x so that the profit is maximum.

Q. solve ∫_1^2▒√(1+1/t^2 +〖(lnt)〗^2+2lnt+1)dt

Q. solve ∫_1^2▒√(1+1/t^2 +〖(lnt)〗^2+2lnt+1)dt

Find the antiderivative of the following:

1. ((3x^2+14x+13)/(x+4) dx
2. ((2x+5)/(3x-1) dx
3. ((x^5-2x^3-2x)/(x^2+1) dx
4. ((x^3+4x)/(x^2-1) dx

Find the antiderivative of (1+e^x)/(1-e^x) dx

Find the anti derivative of sqrt of (x^4-2x^3+x^2)

How many points lie on plane curves 2 2
+ 1
9 4
x y = and 2 2 ( 1) 1
16 9
x y + − = ?
(a) 1 (b) 2 (c) 3 (d) 4 (e) 0

Given two points A (1,2,3), B (7,6,5), let S be the set of all points in (x, y)–plane
such that X
PA is orthogonal to X
PB, then
(a) S is empty
(b) S contains exactly one point
(c) S contains exactly two points
(d) S is a line segment
(e) S is a circle

Add using trigonometry (cosine and sine law) 7 m/s on a bearing of 030° and 2 m/s from a bearing of 343°.