Calculus Answers

Two curves having an equation of x=2√y and y=2√x intersect each

other. Compute the area between the two curves.

Find an equation of the line through the point (3, 5) that cuts off the least area from the first quadrant?

a) A plant grows 1.6 cm in the first week. Each week it grows by 5% more than it did the week before. Using geometric sequence find, how much it grows in the 6^th week.

b) In the year 2000 a shop sold 150 computers. Each year the shop sold 10 more computers than the year before. Show that the shop sold 220 computers in 2007.

c) How many students must be in a class to guarantee that at least two students receive the same score on the final exam if the exam is graded on a scale from 0 to 100 points?

Identify the surfaces of the following equations by converting them into equations in the Cartesian form.

ρ = sin ϕ sin θ

find the area enclosed by the curve r^2=4cos theta

Given the area in the first quadrant bounded by x² = = 8y, the line

y-2 and the y-axis. What is the volume generated when this area is

revolved about the line y - 2 = 0?

Given the area in the first quadrant bounded by x² = 8y, the line

x=4 and the x-axis. What is the

the volume generated by revolving this

area about the y-axis?

Find the volume by revolving the hyperbola xy = 6 from x=2 to x=4

about the x-axis.

Find the length of arc of the curve 𝑦 = 𝑥 3⁄2 /√3 from (0, 0) to (4, √8 / 3 )

A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards the wall at the rate of 20 m/min, how fast is the top of the ladder moving up the wall when the top of the ladder is 6 meters from the ground?