# MCV4U1 Introduction to Calculus – Limits

Assignment Requirement/Question file (UA530)

##### PART A: Knowledge (26 marks)
1. For the function: π(π₯) = π₯3 β 4π₯ + 1, find the slope of the secant line between the points where x=2 and x=5.

[3]

2.Given the function π(π₯) = 3π₯2β4π₯+1

π₯β1

[4]

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

π₯β1 π₯β1

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

a) limβ π(π₯) b) lim+ π(π₯)

π₯β1 π₯β1

c) lim π(π₯) d) f(2)

π₯β2

e) lim π(π₯)

π₯β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 π¦

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) π₯limβ4 π₯ 3βπ₯π₯2ββ144 π₯+8

[2,3]

4π₯ β 3 , π₯ β€ 0

e) lim π(π₯) when π(π₯) = {β2 + π₯2 , π₯ > 0}

π₯β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) limβ |π₯+8|π₯ b)

π₯ββ8 π₯+8 π₯β 5π₯β8

5

[2,2]

c) lim

π₯β3 π₯β3

[3]

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

π₯2 β π, π₯ β€ 5

π(π₯) = {π₯2βππ₯β30

, π₯ > 5

π₯β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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