# MCV4U1 Introduction to Calculus – Limits

Assignment Requirement/Question file (UA530)

##### PART A: Knowledge (26 marks)
1. For the function: 𝑓(𝑥) = 𝑥3 − 4𝑥 + 1, find the slope of the secant line between the points where x=2 and x=5.

[3]

2.Given the function 𝑓(𝑥) = 3𝑥2−4𝑥+1

𝑥−1

[4]

1. For what value of xis f(x) not continuous?
1. Give a reason why it is discontinuous.
1. Find lim 3𝑥2−4𝑥+1 d) Sketch the function

𝑥→1 𝑥−1

1. Refer to the graph of y = f(x) and determine [4]

a) lim𝑓(𝑥) b) lim+ 𝑓(𝑥)

𝑥→1 𝑥→1

c) lim 𝑓(𝑥) d) f(2)

𝑥→2

e) lim 𝑓(𝑥)

𝑥→4

f) Use conditions studies in class to explain why f(x)is not continuous at x=2.

1. Find the equation of the tangent to the curve 𝑦

Use first principles.

[5]

at the point where x=3.

1. Find the following limits.
1. 1 19 lim2x3 -7x+6 b) lim x

x

[1,2]

x2 2x15

c) xlim 3 2x2

x d) 𝑥lim→4 𝑥 3−𝑥𝑥2−−144 𝑥+8

[2,3]

4𝑥 − 3 , 𝑥 ≤ 0

e) lim 𝑓(𝑥) when 𝑓(𝑥) = {−2 + 𝑥2 , 𝑥 > 0}

𝑥→0

[2]

##### PART B: Application (7 marks)

[7] 6.A rock thrown vertically upward from the surface of the moon at a velocity of 24 m/s reaches a height of s(t) = 24t– 0.8t2 metres in tseconds.

1. Determine the average velocity from t= 12 s to t= 17 s
1. Find the velocity at t= 18 s
1. Is the rock rising or falling at t= 18 s? How do you know?
##### PART C: TIPS (11 marks)

7. Find the following limits. If the limit does not exist, explain why not.

a) lim|𝑥+8|𝑥 b)

𝑥→−8 𝑥+8 𝑥→ 5𝑥−8

5

[2,2]

c) lim

𝑥→3 𝑥−3

[3]

8. Find the constants a and b so that the function:

𝑥2 − 𝑎, 𝑥 ≤ 5

𝑓(𝑥) = {𝑥2−𝑏𝑥−30

, 𝑥 > 5

𝑥−5

is continuous for all x .

[4]

##### PART D: Communication (8 marks)

9. Explain how to find the instantaneous rate of change at a point when only the graph of the relation is given.

[2]

10. Identify three types of discontinuities and give an example of each (either a function or a diagram). In each case, does the limit at the point exist?

[6]

Assignment Solution/Sample Assignment

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