Calculus Answers

Q3

Insurance Premiums An insurance company has a simplified method for determining the annual premium for a term life insurance policy. A flat annual fee of $ 150 is charged for all policies plus $2.50 for each thousand dollars of the amount of the policy. For example, a $20,000 policy cost $150 for the fixed fee plus $50, which corresponds to the face value of the policy. ( stated in thousands of dollars ) , determine the function which can be used to compute annual premiums. 

Q1

Membership Drive A small health club is trying to stimulate new memberships. For a limited time, the normal annual fee of $300 per year will be reduced to $200. As an additional incentive, for each new member in excess of 60, the annual charge for each new member will be further reduced by $2. Determine the function p = f(n), where p equals the memberships fee for new members and n equals the number of new members.

Given that y = x is a particular solution of the differential

equation y''-x2y'

+ xy = 0. Find its general solution.

"x^2-xy+y^2=3" is the equation of an ellipse. By implicit differentiation determine the equation of the normal of the given equation at (-1,1)

The equation of the ellipse is given as "(x\/a)^2+(y\/b)^2 =1"

find the equation of the tangent at (x₀, y₀)

Calculate all second order derivatives of g(x,y)= xsin(x+y)+e^y

Use a triple integral to determine the volume of the region bounded by z =

p

x

2 + y

2 and z = x

2 + y

2

In 1st octant

from the top of a 60m tall lighthouse, the angle of depression of a ship moving east away from the lighthouse at 8kmph is 15 degrees. Calculate the angle of depression of the ship from the top of the lighthouse two minutes later, given that the ship stays on the same course at the same speed.