Calculus Answers

A rectangle has its base on the x-axis and its upper two vertices on the parabola y=12-x^2.

Write a formula for the area as a function of x in the form A=a+bx+cx^2+dx^3 where a, b, c and d are integers (some may be zero).

Find the area of the region inside the circle r=2sinθ and outside the circle r=1.

Find the area enclosed by the curve r(θ)=1+2sinθ and the rays θ=0 and θ=π/3

The equation of the tangent plane to h(x,y)=yln(x) at the point (1,5) is
Select one:
a. z=1/5x+1/5y

b. z=x+y


c. z=1/4x+1/4y


d. z=4(x−1)


e. z=5(x+1)


f. z=5(x−1)

A triangular lamina in the Ty-plane such tha
its vertices are (0,0), (0,1) and (1,0). Suppose

that the density function of the lamina is
y) = 63ry g
defined by p(x.
centimetre. Use the information given to
answer the following questions (2 decimal
places):

The total mass of the lamina is
grams.
The moment about the x -axis of the lamina

The Moment about the y -axis of the lamina

The centre of gravity of the lamina ( x, y) is (

The equation of the tangent plane to h(x,y)=yln(x) at the point (1,5) is
Select one:
a. z=1/5x+1/5y

b. z=x+y


c. z=1/4x+1/4y


d. z=4(x−1)


e. z=5(x+1)


f. z=5(x−1)

A triangular lamina in the xy -plane such that its vertices are (0,0), (0,1) and (1,0). Suppose that the density function of the lamina is defined by p(x,y)=120xy. What is the total mass of the lamina and the center of gravity?

The equation of the tangent plane to h(x,y)=yln(x) at the point (1,5) is
Select one:
a. z=1/5x+1/5y

b. z=x+y


c. z=1/4x+1/4y


d. z=4(x−1)


e. z=5(x+1)


f. z=5(x−1)

Find the area bounded by y=cosx, the x-axis and between x=−π2 to x=π2. Draw a sketch for yourself to help you find the integral.