Indicated Derivatives - Calculus - Exam, Exams of Calculus

This is the Exam of Calculus Indefinite Integrals, Limits, Explanation, Curve Parametrized, Involve the Variables etc. Key important points are: Indicated, Derivatives, Functions, Simplify, Graphs, Four Function, Spaces, Planation is Required, Curve, Implicit Di Erentiation

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2012/2013

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MATH 150
Midterm 2, November 3, 2005
Last Name:
First Name:
SFU Student email : @sfu.ca
1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.
2. Circle your instructor. If you don’t, you lose a mark.
3. This test is comprised of 8 pages.
4. Once the test begins, please check that all pages are intact.
5. Do ALL questions.
6. Clearly explain your answer. No credit will be given for just
writing down the answer.
7. If the answer space provided is not sufficient, write your answer
on the back of the previous page. Clearly mark the question
number.
8. Ordinary Scientific Calculators ONLY are allowed.
NO GRAPHING CALCULATORS ALLOWED.
Question Score Max
1 7
2 4
3 9
4 6
5 4
Total 30
Page 1 of 8
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MATH 150

Midterm 2, November 3, 2005

Last Name:

First Name:

SFU Student email : @sfu.ca

1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.

2. Circle your instructor. If you don’t, you lose a mark.

3. This test is comprised of 8 pages.

4. Once the test begins, please check that all pages are intact.

5. Do ALL questions.

6. Clearly explain your answer. No credit will be given for just

writing down the answer.

7. If the answer space provided is not sufficient, write your answer

on the back of the previous page. Clearly mark the question

number.

8. Ordinary Scientific Calculators ONLY are allowed.

NO GRAPHING CALCULATORS ALLOWED.

Question Score Max

Total 30

  1. Find the indicated derivatives of the following functions. You do not need to simplify your answers.

(1a) (4 marks) y ′^ and y ′′^ where y = e

sin(2x)

Answer

y ′=

y ′′=

  1. A particle travels along a straight line. The distance s (in metres) the particle is from the origin 0 at time t (in seconds) is given by

s(t) = t^4 − 4 t^3 + 2

(2a) (1 mark) Find the velocity and acceleration at time t.

Answer

(2b) (3 marks) When is the particle speeding up? When is the particle slowing down?

Answer

  1. Consider the curve defined by x^2 − y^2 = xy + 1.

(3a) (1 mark) Show that (1, −1) and (− 1 , 1) lie on the curve.

Answer

(3b) (1 mark) Find another point on the curve different from the points in (3a).

Answer

  1. (6 marks) You are driving in a car at 60 km/hr towards the place where a rocket has recently been launched. You see the rocket directly in front of you at altitude θ (see diagram). It is travelling at 300 km/hr vertically. When you are 10 km from the launch pad the rocket is at height 30 km. At what rate do you see the altitude of the rocket changing at that time?

Answer

  1. (4 marks) Use the linear approximation of f (x) at x = 3 to estimate f (3.05) where

f (x) = x

8 x + 1.

Answer