MATH-1036EL Study Guide - Final Guide: Mean Value Theorem, Laurentian University
25 Jun 2018
School
Department
Course
Professor
LAURENTIAN UNIVERSITY
UNIVERSIT´
E LAURENTIENNE
Dec. 16, 2010 - 9:00 am Course and No. MATH 1036EL 01 & 02
Date ................................... Cours et no ...........................
Total no. of pages
Nombre total de pages ........... questions...........
Professor T. Markovich/N. Robidoux Time allowed 3 hours
Professeur................................. Dur´ee de l’examen......................
Other instructions
Autres directives
Attention
Do not use exam booklets.
The exam consist of two parts.
The first part is multiple choice and consists of 15 questions, 2 marks for each question. In each multiple choice
question, circle one and only one of the letters a,b,c,d or e which you consider the correct answer. There is no
penalty for guessing.
The second part consists of questions and is worth marks. Each question in this part should be answered
in the space provided and you should show all your work.
There are questions in total. Make sure your booklet is complete.
Only non-programmable caclculators are allowed.
Answer all questions on this questionnaire.
d Marks [ ] for each question are indicated in the margin. Total Marks: .
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Dec. 16, 2010 - 9:00 am MATH 1036EL 01 & 02 1
Part I (30 marks)
1. Given that cos θ=−1
3for π < θ < 3π
2, the value of cot θis:
(a) −3
2√2
(b) 2√2
(c) 1
2√2
(d) −2√2
3
(e) −3
2. The value of lim
x→2
x2+x−6
x−2is
(a) ∞
(b) −∞
(c) 0
(d) 5
(e) −5
3. The value of cso that
f(x) = (cx2+ 2 if x < 2
x3−cx if x≥2
is continuous on (−∞,∞) is
(a) 2
3
(b) 3
2
(c) 3
4
(d) 4
3
(e) none of the above
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Dec. 16, 2010 - 9:00 am MATH 1036EL 01 & 02 2
4. If f(x) = √x g(x) and g(4) = 8 and g′(4) = 7, then f′(4) is:
(a) 13
(b) 11
(c) 4
(d) 12
(e) 16
5. Suppose that F(x) = f(g(x)) and g(2) = 4, f′(4) = 4, g′(2) = 2. Then by the
chain rule F′(2) is:
(a) 8
(b) 6
(c) 24
(d) 44
(e) 42
6. If f(x) = 1
xthen f(10)(x) is:
(a) 9!x10
(b) 9!
x10
(c) −(10!)
x11
(d) 10!
x11
(e) −(9!)
x10
7. The absolute maximum value of f(x) = x2(2 −x) on the interval [0,3] is:
(a) 0
(b) 12
37
(c) 32
37
(d) -9
(e) 4
3
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Document Summary
The rst part is multiple choice and consists of 15 questions, 2 marks for each question. In each multiple choice question, circle one and only one of the letters a,b,c,d or e which you consider the correct answer. The second part consists of in the space provided and you should show all your work. questions and is worth marks. Each question in this part should be answered. Answer all questions on this questionnaire. d marks [ ] for each question are indicated in the margin. Part i (30 marks: given that cos = . , the value of cot is: (c) 3 (b) (c) (d) (e) none of the above. Then by the chain rule f (2) is: (a) 8 (b) 6 (c) 24 (d) 44 (e) 42: if f (x) = 1 x then f (10)(x) is: (a) 9!x10 (b)
