Chapter Limits Review
Chapter
Chapter 1
Section
Chapter Limits Review
Solutions 20 Videos

The general term of a sequence is given by \displaystyle t_n = \frac{3- n^2}{3n}, n \in \mathbb{N} 

a) Write the first five terms of this sequence.

b) Does this sequence have a limit as n \to \infty?

Q5

A bouncy ball is dropped from a height of 5 m. It bounces \frac{7}{8} of the height after each fall.

a) Find the first five terms of the infinite sequence representing the vertical height travelled by the ball.

b) What is the limit of the heights as the number of bounces approaches infinity?

c) How many bounces are necessary for the bounce to be less than 1 m?

Q6

Determine whether the function \displaystyle g(x) = \frac{x-5}{x + 3}  is continuous at x =3. Justify your answer using a table of values.

b) Is the function in part a) discontinuous for any number x? Justify your answer.

Q7

Examine the following graph.

State the domain and range of this function

Q8a

Evaluate each of the following limits for this function.

i. \displaystyle \lim_{x\to + \infty} \frac{-2x^2 + 8x -4}{x^2} 

ii. \displaystyle \lim_{x\to - \infty} \frac{-2x^2 + 8x -4}{x^2} 

iii. \displaystyle \lim_{x\to 0^+} \frac{-2x^2 + 8x -4}{x^2} 

iv. \displaystyle \lim_{x\to 0^-} \frac{-2x^2 + 8x -4}{x^2} 

Q8b

Evaluate each limit, if it exists.

\displaystyle \lim_{x\to -1} \frac{(-1 + x)^2 -4}{x + 1} 

Q9a

Evaluate each limit, if it exists.

\displaystyle \lim_{x\to 3} \frac{-x^2 + 8x}{2x + 1} 

Q9b

Evaluate each limit, if it exists.

\displaystyle \lim_{x\to 0} \frac{\sqrt{x + 16}} -4{x} 

Q9c

Evaluate each limit, if it exists.

\displaystyle \lim_{x\to 0} \frac{3x^2 + 5x -2}{x^2 -2x -8} 

Q9d

Evaluate each limit, if it exists.

\displaystyle \lim_{x\to 7} \frac{x^2 -49}{x -7} 

Q9e

What is true about the graph of y = f(x) if

\lim{x\to -6^- }f(x) = \lim{x\to -6^+ }f(x) =3, but f(-6) \neq -3 ?

Q10

Use the first principles definition to differentiate each function.

y = 4x -1

h(x) = 11x^2 + 2x