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: 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₯2β4π₯+1
π₯β1
[4]
- For what value of xis f(x) not continuous?
- Give a reason why it is discontinuous.
- Find lim 3π₯2β4π₯+1 d) Sketch the function
π₯β1 π₯β1
Refer to the graph of y = f(x) and determine [4]
a) limβ π(π₯) b) lim+ π(π₯)
π₯β1 π₯β1
c) lim π(π₯) d) f(2)
π₯β2
e) lim π(π₯)
π₯β4
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 π¦
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) π₯limβ4 π₯ 3βπ₯π₯2ββ144 π₯+8
[2,3]
4π₯ β 3 , π₯ β€ 0
e) lim π(π₯) when π(π₯) = {β2 + π₯2 , π₯ > 0}
π₯β0
[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) limβ |π₯+8|π₯ b)
π₯ββ8 π₯+8 π₯β 5π₯β8
5
[2,2]
c) lim
π₯β3 π₯β3
[3]
8. Find the constants a and b so that the function:
π₯2 β π, π₯ β€ 5
π(π₯) = {π₯2βππ₯β30
, π₯ > 5
π₯β5
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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