MATH1013 Final Mock Test

All Sections

1. Show that the equation has at most one root on the interval [ ]

Section C only

2. Newton’s law of gravitation says that the magnitude F of the force exerted by a body of

mass m on a body of mass M is:

Where G is the universal gravitational constant and r is the distance between the two

bodies.

a) Find

. What does the negative sign indicate?

b) Suppose it is known that the Earth attracts an object with a force that decreases at a

rate of 0.5N/m when an object is away. How fast does the force change when

?

Section D only

3. If two resistors with resistances are connected in parallel, then the total

resistance R, measured in Ω is given by:

If are increasing at a rate of

respectively, how fast is R changing when

?

All Sections

4. Sketch the curve.

All Sections

5. Find the limits by use of l’Hopital’s Rule.

a)

b) BONUS: ( )

All Sections

6. Find the maximum possible value for a cylinder inscribed in a sphere of radius r.

All Sections

7. Find the most general anti derivatives

a) ( )

√

b) ( )

Sections A and B only

8. Evaluate the Riemann sum for ( ) with:

NOTE to all sections!

The parts of the book that were not covered for certain sections include 3.5, 3.8, 5.1, 5.3.

The chapter 3 sections were covered in some of my other mock tests on the facebook page.

https://www.facebook.com/groups/161813664012727/

The chapter 5 sections should be studied by yourself because they will be covered on your test

and/or final exam!

The rest of this page is to be used for rough notes for any problem in this mock test.