Test 3

(a) A graph of the function is given below

Fill in the following table with approximate values (if they exist)

2 4 6 8 10 12 14

(b) For the function

find and an equation of the tangent line to

the graph of the above function at

In the questions c to h , find

(C )

(d) You may use

(e)

(f)

(g) (2Find if

i.e.

(2) (a) Find an equation of the tangent line to the graph of

y=2^x cosxat (0,1)

Use geogebra or any other tool to draw a graph

of y=2^x cosxand that of the tangent line to the graph of

y=2^x cosxat (0,1)in the same window.

(b) Find an equation to the tangent line to the graph of

at

Use geogebra or any other tool to draw a graph

of and that of the tangent line to the graph of at

in the same window.

(c) We are given the graphs of and below. Find , i.e. the derivative of at 1.

(d) Find the differential of . Find , an equation of the tangent line to the graph of at

Two cars start moving from the same point. One travels east at a constant rate of 60 miles per hour and the other travels north at a

constant rate of 70 miles per hour. Find the rate at which the distance between the cars is changing 1 hour later. You may round your answer to

two digits after the decimal sign.

(e) Find if and find an equation of the tangent line to the graph of at

(f) Find an equation of the tangent line to the graph of

at

(g) Use Newton’s method to find the solution of

by using the following steps

(i) Find, where

(ii) Find, where

(iii) Choose a guess point

(iv) Perform the iterations, until the values stabilize to the 8-dgits after the decimal sign.