Calculus Answers

A parabola has an equation of . If the area is revolved about the line y = 0, what is the resulting volume generated?

Evaluate subject to the functional relation x=t³ and y=t².

Find the volume generated by rotating the region bounded by y = x, x = 1, and y² = 4x, about the x-axis.

using weierstrass m-test show that the following series converges uniformly∑ n=1 ∞ n^3 X^n,X€[-1/3,1/3]

use cauchy's mean value theorem to prove that {cosa-cosB/sina-sinB}=tan0,0<a<0<B<π/2

Solve the integral of √(49-x²)÷x from ln1 to ln2, using trigonometric substitution.

Solve the integral of √(49-x²)÷x from ln1 to ln2

Question 1

Find the derivative of

y = ln 3x⁵.

a.    ln 3x⁵

b.    15x⁴

c.    5x⁻¹

d. 1/

3x⁵

Question  2

Find the derivative of the function

a.    x²_/ x + x_/ x

b. x² + x /x

c. 2x + 1

d.    3x⁴ + 2x³

Question  3

Differentiate the function

f (x) = 3x³e^2x.

a. 5x⁴e^3x

b. 3x²e^2x(x − 3)

c. 3e^3x + 9x⁴x⁵

d. 3x²e^2x(2x + 3)

Question  4

The total revenue function (TR), in terms of P and the company's quantity, if a commodity sells for R199.00  are?

a. TR = 6 000 − 30P ; Q = 30.

b. TR = 6 000P − 30P ²; Q = 30.

c. TR = P (6 000 − 30P ); Q = 24.

d.  TR = 6 000 − 30P ; Q = 24.

Find the domain and range of f(x,y)= 2xy/x^2+y^2

(D − 1)^2(D^2 + 1)^2 y = sin^2(x/2) + e^x + x