Calculus Answers

1. Calculate the turning points of the function y=sin3t using differential calculus
2. Show which are maxima, minima or points of inflexion using the second derivative

 Determine the limits if they exist for the function lim (x,y)→(0,0) 1 − x − y /x 2 + y 2

f^(7) (x) of y = x^-2

y'' of y = x^-2 at x=2

Derivative of x^3+4xy^2+5y^3=1 at (2,-1)

Express the height of a cylindrical can as a function of the diameter, if 18pi sq.in. of sheet metal is used. H=?

.A geometric series with first term 3 converges to the sum of 2. Find the common ratio of the series.

3)

You plan to make a simple, open topped box from a piece of sheet metal by cutting a square – of equal size – from each corner and folding up the sides

If 𝑙 = 200𝑚𝑚 and 𝑤 = 150𝑚𝑚 calculate:

a) The value of x which will give the maximum volume

b) The maximum volume of the box

c) Comment of the value obtained in part b.

4) The gain of an amplifier is found to be

𝑮 = 𝟐𝟎 𝐥𝐨𝐠(𝟏𝟎𝑽𝒐𝒖𝒕):

The tasks are to find equations for:

a) 𝑑𝐺/𝑑𝑉𝑂𝑢𝑡

b) 𝑑^2𝐺/𝑑𝑉𝑂𝑢𝑡 2