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 /26	Inquiry/Thinking /11	Communication /8	Application /7

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

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

^{a) lim}− ^{𝑓(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.

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

Use first principles.

[5]

at the point where x=3.

3. Find the following limits.

3. 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 + 𝑥}2 ^{, 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

2. Find the velocity at t= 18 s

3. 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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