Calculus Answers

Find the volume generated if the region enclosed by y = x² and the line y = 2x is revolve about the x-axis. Answer in 2 decimal places.

Find the volume of the solid obtained by rotating the region bounded by y = x^2 +1 and y = 9 – x^2 about y = -1.

A piece of string whose length is 32cm is cut into 2 pieces. one piece is used to form an equilateral triangle and the other to form of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express your answer in pi. What is the function

Computation of derivative

Computation of Critical numbers

Computation of minimum value

Represent the sum of first terms of the series 3+33+333+.........

using the sigma notation.

Differentiate y= cos (6x +2)

Find the absolute maxima and minima of the function on the given domain

T(x, y) = x

2 + xy + y

2 − 6x + 2 on the rectangular plane 0 ≤ x ≤ 5, −3 ≤ y ≤ 3.

If dy/dx= x-x²/2x⁴ and y=2 when x=1 to express y in terms of x.

A tumor is injected with 0.9

 grams of Iodine-125, which has a decay rate of 1.15%

 per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t

 days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60

 days.