MATH 151 Midterm 2: Derivatives, Implicit Differentiation, Tangent Lines (Nov 2, 2005), Exams of Calculus

The midterm exam for math 151, held on november 2, 2005. The exam covers topics such as derivatives, implicit differentiation, and finding equations of tangent lines. Students are required to find derivatives of given functions, identify graphs of functions and their derivatives, and solve problems related to curves and angles between moving objects.

Typology: Exams

2012/2013

Uploaded on 02/18/2013

akshaya
akshaya 🇮🇳

4.5

(39)

88 documents

1 / 8

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
MATH 151
Midterm 2, November 2, 2005
Last Name:
First Name:
SFU Student email : @sfu.ca
Section Instructor: N. Bruin / R. Choksi / R. Pyke
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
pf3
pf4
pf5
pf8

Partial preview of the text

Download MATH 151 Midterm 2: Derivatives, Implicit Differentiation, Tangent Lines (Nov 2, 2005) and more Exams Calculus in PDF only on Docsity!

MATH 151

Midterm 2, November 2, 2005

Last Name:

First Name:

SFU Student email : @sfu.ca

Section Instructor: N. Bruin / R. Choksi / R. Pyke

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 = cos(e^2 x)

Answer

y ′=

y ′′=

  1. (4 marks) Below are the graphs of four functions. Among them are the graphs of f (x), f ′(x) and f ′′(x). Determine which of the graphs are the graphs of f (x), f ′(x) and f ′′(x) and fill in the spaces below with your choice of a, b, c or d. (No explanation is required.)

Answer

f :

f ′^ :

f ′′^ :

0

20

40

60

y

–3 –2 –1 1 2 3 4 x

0

20

40

60

y

–3 –2 –1 1 2 3 4 x

a b

0

20

40

60

y

–3 –2 –1 1 2 3 4 x

0

20

40

60

y

–3 –2 –1 1 2 3 4 x

c d

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

(3a) (1 mark) Show that (0, 0) lies on the curve.

Answer

(3b) (2 marks) Use implicit differentiation to find y ′.

Answer

(3c) (2 marks) Find the equation of the tangent line at a point (a, b) on the curve (your answer should contain a and b).

Answer

  1. (6 marks) Two people A and B are walking along straight lines that meet at a right angle (see diagram). A approaches the intersection at 2m/s, while B moves away from the intersection at 1m/s. At what rate is the angle θ changing when A is 10m from the intersection and B is 20m from the intersection?

A

B

θ

Answer

  1. (4 marks) Use the linear approximation of f (x) at x = 9 to estimate f (9.01) where

f (x) =

x +

x

Answer