MATH 154 Midterm 2: Solutions for Function Derivatives and Applications, Exams of Calculus

The midterm 2 exam for math 154 - calculus i at simon fraser university, instructed by d. Kent. The exam covers topics such as finding 'y' for given functions, differentiable functions, equations of tangent lines, spherical balloon radius, implicit functions, and radioactive material decay. Students are required to show all work and follow instructions carefully.

Typology: Exams

2012/2013

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Simon Fraser University
MATH 154 โ€“ MIDTERM 2
Instructor: D.Kent
November 9, 2005
Last Name____________________________
Given Name(s)________________________
Student ID____________________________
Signature____________________________
Question Maximum Mark
1 15
2 3
3 4
4 3
5 5
6 4
7 2
8 4
Total 40
INSTRUCTIONS
1. Do not open this booklet until
instructed to do so. The booklet contains
8 pages including the cover page.
2. Print your name and student ID in the
space provided above.
3. For each question you must show all
your work unless stated otherwise.
4. No book, paper, or device other than the
usual writing instruments, this booklet, and
scientific calculators are allowed. In
particular, no graphing/programmable
calculators are allowed.
5. During this examination, speaking to,
communicating with, or exposing written
papers to the view of other students is
forbidden.
6. You may use the back of the previous
page for a rough work or if you run out of
space.
7. Stop writing when you are instructed to
do so. Failure to follow instructions may
result in penalties.
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Simon Fraser University

MATH 154 โ€“ MIDTERM 2

Instructor: D.Kent

November 9, 2005

Last Name____________________________

Given Name(s)________________________

Student ID____________________________

Signature____________________________

Question Maximum Mark

Total 40

INSTRUCTIONS

1. Do not open this booklet until instructed to do so. The booklet contains 8 pages including the cover page.

  1. Print your name and student ID in the space provided above.
  2. For each question you must show all your work unless stated otherwise.
  3. No book, paper, or device other than the usual writing instruments, this booklet, and scientific calculators are allowed. In particular, no graphing/programmable calculators are allowed.
  4. During this examination, speaking to, communicating with, or exposing written papers to the view of other students is forbidden.
  5. You may use the back of the previous page for a rough work or if you run out of space.
  6. Stop writing when you are instructed to do so. Failure to follow instructions may result in penalties.

1. [15 marks total] Find y 'for given function y = f ( ) x ( DO NOT SIMPLIFY ):

a) [3 marks] (^3 2 )

2

x x

y x โˆ’ +

=

b) [4 marks] y = ( 1 โˆ’ x^2 + 23 โˆ’ x )^2

c) [4 marks] y = (1 โˆ’ x )(2 + tan 3 ) x e 2 โˆ’ x

  1. [4 marks] Find the equation of two straight lines of slope m = โˆ’ 2 that are tangent to the curve y =1/ x.
  2. [3 marks] A spherical air balloon is being inflated at a constant rate

k (cm^3 / s ). At what rate is the radius of the balloon increasing when it is L (cm ) long.

  1. [5 marks] Find the second derivative

2 2

y

d x

d of a function that is defined

implicitly by the equation

y x ( )

x^2^ โˆ’ xy + y^2 = 9

6. [4 marks] Use linear approximation to evaluate (0.98)^25.