MCV4U1 Introduction to Calculus – Limits

Assignment Requirement/Question file (UA530)

Full Name:Date:
Full solutions must be shown for full marks Non-programmable calculators are permitted Solutions must demonstrate methods shown in class All solutions must be written in space provided
Mark: /52
Knowledge /26Inquiry/Thinking /11Communication /8Application /7
PART A: Knowledge (26 marks)
  1. For the function: 𝑓(π‘₯) = π‘₯3 βˆ’ 4π‘₯ + 1, find the slope of the secant line between the points where x=2 and x=5.


2.Given the function 𝑓(π‘₯) = 3π‘₯2βˆ’4π‘₯+1



  1. For what value of xis f(x) not continuous?
  1. Give a reason why it is discontinuous.
  1. Find lim 3π‘₯2βˆ’4π‘₯+1 d) Sketch the function

π‘₯β†’1 π‘₯βˆ’1

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

a) limβˆ’ 𝑓(π‘₯) b) lim+ 𝑓(π‘₯)

π‘₯β†’1 π‘₯β†’1

c) lim 𝑓(π‘₯) d) f(2)


e) lim 𝑓(π‘₯)


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.


at the point where x=3.

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



x2 2x15

c) xlim 3 2x2

x d) π‘₯limβ†’4 π‘₯ 3βˆ’π‘₯π‘₯2βˆ’βˆ’144 π‘₯+8


4π‘₯ βˆ’ 3 , π‘₯ ≀ 0

e) lim 𝑓(π‘₯) when 𝑓(π‘₯) = {βˆ’2 + π‘₯2 , π‘₯ > 0}



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) limβˆ’ |π‘₯+8|π‘₯ b)

π‘₯β†’βˆ’8 π‘₯+8 π‘₯β†’ 5π‘₯βˆ’8



c) lim

π‘₯β†’3 π‘₯βˆ’3


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

π‘₯2 βˆ’ π‘Ž, π‘₯ ≀ 5

𝑓(π‘₯) = {π‘₯2βˆ’π‘π‘₯βˆ’30

, π‘₯ > 5


is continuous for all x .


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.


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?


Assignment Solution/Sample Assignment

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