Calculus Answers

A price p (in dollars) and demand x for a product are related by
2x2+7xp+50p2=21600.

If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand.

Rate of change of demand =

Gravel is being dumped from a conveyor belt at a rate of 30ft^3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 10 ft high?

Kaylee has 283 cards she needs 2,988 cards how many more does she need?

differentiate the following products and quotients using algebraic simplification:

f(x) = x ( 1 – x + 3x²)

f(x) = (4x-2x^2+6)/2x

There are 3 parcels, X,Y and Z, at the post office. The average mass of Parcel X, Parcel Y and Parcel Z is 27.4kg. The mass of Parcel Y is trice that of Parcel Z. Parcel X is 3.2kg lighter than Parcel Y. Find the average mass of Parcel Y and Parcel Z.

Give the interval where each of the functions is continuous. Explain your answers.

a. g(x) = (sqrt (x + 1)) / (x^2 - 9)

b. h(x) = ln(x^2 - 1)

c. h(x) = x^2 + 1 if x < -1
= x^2 + 2x + 3 if -1 <= x <= 0
= 1 - (1 / x) if x > 0

The diagram shows part of the curve y=2-18/(2x+3), which crosses the x-axis at A and the y-axis at B. The normal to the curve at A crosses the y-axis at C.
(i) Show that the equation of the line AC is 9x+4y=27.
(ii) Find the length of BC.

The diagram shows the curve y=6x-x^2 and the line y=5. Find the area of the shaded region.

1. Let A={1,2,3,4} and B={a,b,c}.
(i) Write down a function from A to B
(ii) Write down a different function from A to B
(iii) Write down a relation from A to B which is not a function
(iv) How many functions are there from A to B?

2. Determine whether each of the statements that follow are true or false. If the statement is true, give a reason. If it is false, give a counterexample (i.e. a function for which the statement is false)
(i) The domain of every function is a subset of R.
(ii) If f:R=>R is a function and xER then f(2x) = 2f(x)
(iii) If h:A=>B is a function and a, bEA then h(a) = h(b) implies that a=b

y=x/(x+1)square differentiate it w.r.t x