Full Exam Review - exam Calculus (Ancaster High Secondary School)

Full Exam Review - exam


Calculus (Ancaster High
Secondary School)

, MCV4U CALCULUS - Exam Review
1) Examine the graph of f(x) = 3
.
𝑥2−9
Evaluate each limit for the graph.
3 3
i) 𝑙𝑖𝑚𝑥→3− 2 ii) 𝑙𝑖𝑚𝑥→3+
𝑥 −9 𝑥2−9
3 3
iii) 𝑙𝑖𝑚 iv) 𝑙𝑖𝑚 𝑥→−∞
𝑥→+∞ 𝑥2−9 𝑥2−9


2) Evaluate each limit, if it exists.
a) 𝑙𝑖𝑚 3𝑥2+2𝑥
−8
𝑥→−2

𝑥2
−3
𝑥
−1
0

b) 𝑙𝑖𝑚 √9−𝑥−3
𝑥→0 𝑥
c) 𝑙𝑖𝑚 2
(𝑥−2) −1
𝑥→1 𝑥−1


3) The relationship between the kinetic energy, in Joules, of an object with mass 8 kg and the velocity of
the object, in metres per second, is given by the equation 𝐸𝑘 = 8𝑣2.
a) Determine the average rate of change of energy between velocities of 2 m/s and 5 m/s.
b) Use first principles to find the derivative of the kinetic energy equation.
c) Use the derivative to find the instantaneous rate of change of energy when v = 4 m/s.
𝑑𝑦
4) Find from first principles for:
𝑑𝑥

a) b)

5) For the function 𝑓(𝑥) = 4𝑥2 − 2𝑥 + 1
a) find the slope of the secant from 𝑥 = 1 to 𝑥 = 5
b) find the slope of the tangent at 𝑥 = 1

6) Determine the derivative of each function

a) b)


c) d)



e) f)