UNIT 1 Limits TEST Mathematics (Chino Hills High)

UNIT 1 Limits TEST


Mathematics (Chino Hills
High)

, MCV 4U Test1 Limits, Continuity, Rates of Change. Name: Date:




MCV4U UNIT 1 TEST Limits, Continuity and Rates of Change
**Reminder: Derivatives and L’Hopital Rule are not allowed**

K/U C T/I App




15 10 10 18

Part A – Knowledge/Understanding.
1. Complete the following: [6 marks] You must show work or explain logic for full marks.

a) lim
𝑥→−1+
b) lim 16 =
𝑥 → −4+


c) lim −
6
) =
𝑥→ 1
3− ( 𝑥−3 𝑥2−9




𝑥+3
d) State the equation of all Vertical asymptotes: 𝑓(𝑥) =
(𝑥−2)(𝑥2−9)



e) A function has a hole at the point P(3, 3), and f(3) = 4.
i) Determine: lim 𝑓(𝑥) =
𝑥→3

ii) Explain your reasoning:
2. For 𝑦 = 𝑓(𝑥), the average rate of change from 𝑥 = 𝑎 to 𝑥 = 𝑎 + 𝑏 is calculated as:
𝑓(𝑎+𝑏)−𝑓(𝑏) 𝑓(ℎ)−𝑓(𝑎) 𝑓(𝑎+𝑏)−𝑓(𝑎)
A)
ℎ
B) lim 𝑓(𝑎+ℎ)−𝑓(𝑎) C) D)
ℎ→0 ℎ ℎ 𝑏

3. For the function 𝑓(𝑥), the instantaneous rate of change at 𝑥 = 𝑎 is calculated as:

A) lim 𝑓(𝑎+ℎ)−𝑓(𝑎)
ℎ→𝑎 B) lim 𝑓(𝑎+ℎ)+𝑓(𝑎) C) lim 𝑓(𝑎+ℎ)−𝑓(𝑎) D) lim 𝑓(𝑎+ℎ)+𝑓(𝑎)
ℎ ℎ→𝑎 ℎ ℎ→0 ℎ ℎ→0 ℎ