MCV4U Rates of Change, Limits, and Continuity

Determine the average rate of change between the points

 $\left(-3,2\right)$  and  $\left(5,1\right)$  

•  $\frac{1}{8}$  

•  $-\frac{1}{8}$  

•  $-8$  

•  $8$  

Estimate the instantaneous rate of change at the point indicated on the graph

• 4

• 2

• 1.5

• 3

At which point(s) is the instantaneous rate of change positive (IRoC >0) ?

• Only A

• All points A,B, C, and D

• Only C and D

• Only B, C, and D

Rank the IRoC in order from largest to smallest value

• A, B, C, D

• D, C, B, A

• A, B, D, C

• B, C, D, A

Determine the average rate of change of $y=x^2-3x$  on the interval  $x\in\left[-1,2\right]$ .

•  $-2$  

•  $2$  

•  $-\frac{4}{3}$ 

•  $\frac{2}{3}$  

Estimate the instantaneous rate of change of $y=x^2-3x$  at $x=0$ .

•  $0$  

•  $-3$  

•  $1$ 

•  $-1$  

A ball is thrown into the air and after $t$ seconds its height from the ground (in metres) is given by  $h\left(t\right)$ . The ARoC of  $h\left(t\right)$  on  $t\in\left[0,3\right]$  is  $6$ . What does that mean?

• The speed of the ball at 3 seconds is 6m/s.

• The average speed of the ball over the first 3 seconds is 6 m/s.

• The speed of the ball at 6 seconds is 3 m.

• The average speed of the ball at 3 seconds is 6m.

What is  $\lim_{x\rightarrow2^-}f\left(x\right)$  ?

• 3

• 4

• DNE (does not exist)

• 2

What is  $\lim_{x\rightarrow2^+}f\left(x\right)$  ?

• 3

• 4

• DNE (does not exist)

• 2

What is  $\lim_{x\rightarrow2}f\left(x\right)$  ?

• 3

• 4

• DNE (does not exist)

• 2