# Calculus

**Paper, Order, or Assignment Requirements**

-CALCULUS-

No references needed

8 questions required

Takes about 8-10 pages for solving the questions.

**WIFP ASSIGNMENT THREE**

**2015/2016**

__Task One:__

The function is defined by

for all real values of x except 0.

- Find the coordinates of the points where the graph of the function meets the axes.
- Show that the function has exactly one stationary point whose lies in the interval.
- Use Newton Raphson Method to find the of the stationary point giving your answer correct to 6 decimal places. Determine the nature of the stationary point.
- Find the equations of the linear vertical and horizontal asymptotes for.

- Use your answers from 1-5 to produce a hand drawn sketch of the graph of .

[50

__TASK Two. __

** **

For a given firm let Q stand for the amount produced to meet a market demand. Let P stand for the price per unit of quantity produced. Assume that Q is a differentiable function of P. Let be the total revenue function and the marginal revenue.

- Give the definition of the price elasticity of demand.

Use the definition of to show that if the demand is elastic (i.e. ) then will fall if the price increases; and that if the demand is inelastic

(i.e. ) then will rise as the price increases.

- Given that . Solve the resulting differential equation to find the demand equation if when ,

- Use an expression of as a function of and to find the value of that maximises the total revenue

The supply equation is given by . Use the decimal Search method to find the equilibrium price giving your answer correct to five decimal places.

[50]

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