
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)
- 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]
- For what value of xis f(x) not continuous?
- Give a reason why it is discontinuous.
- Find lim 3𝑥2−4𝑥+1 d) Sketch the function
𝑥→1 𝑥−1
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.
- Find the equation of the tangent to the curve 𝑦
Use first principles.
[5]
at the point where x=3.
- Find the following limits.
- 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.
- Determine the average velocity from t= 12 s to t= 17 s
- Find the velocity at t= 18 s
- 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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