Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Series And Functions, MCQ-Calculus for Engineers-Assignment, Exercises of Calculus for Engineers

Institute of Mathematics and ApplicationsCalculus for Engineers

This assignment is for Calculus for Engineers course. It was assigned by Prof. Adesh Rangarajan at Institute of Mathematics and Applications. It includes: Series, Function, Polar, Curves, Taylor, Equation, Interval, origin, Point, Represent, Fourier, Extension, Graph

Typology: Exercises

2011/2012

Uploaded on 07/23/2012

tushaar
tushaar 🇮🇳

4

(4)

20 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Calculus II Assignment 07 April 3, 2009
Assignment – due on April 7, 2009.
Assignments will be collected in the class at the start of the lecture.
Late assignment will not be acceptable. No relaxation in policies.
(See “policies for assignments” on margala/yahoo group)
Question # 1
A. State whether the statements are true or false.
1. If
11
then
0
lim
n
n
2. The polar curves
2sin1r
and
12sin
r
have the same graph.
3. The Taylor series of
x
e
is
...
!3!2
132 xx
x
4. The equation
0
represents a point in the polar plane.
5. It is possible to find a sin series of an even function defined on a symmetric
interval about origin.
B. Choose the best answers
1. The graph of the curve
2sec
2r
is symmetric about
a) x-axis b) y-axis c) origin d) none
2. The period of the Fourier series extension of a function defined on the interval
x0
is
a)
b)
2
c)
2
d)
4
3. The graph of the equation
sectanr
is
a) a circle b) cardioid c) straight line d) spiral
4. The function
xx
xx
xf 0sin
0cos
)(
is
a) an even function b) odd function c) both d) none
5. The graph of the equation
tansin2r
is symmetric about
a) x-axis b) y-axis c) origin d) none
docsity.com
pf2

Partial preview of the text

Download Series And Functions, MCQ-Calculus for Engineers-Assignment and more Exercises Calculus for Engineers in PDF only on Docsity!

Calculus II Assignment 07 April 3, 2009

Assignment – due on April 7, 2009. Assignments will be collected in the class at the start of the lecture. Late assignment will not be acceptable. No relaxation in policies. (See “policies for assignments” on margala/yahoo group)

Question # 1 A. State whether the statements are true or false.

1. If  1  1 thenlim n  ^ n  0

2. The polar curves r  1 sin 2  and r sin 2  1 have the same graph.

  1. The Taylor series of ex is ... 2! 3!

2 3     

x x x

  1. The equation  0 represents a point in the polar plane.
  2. It is possible to find a sin series of an even function defined on a symmetric interval about origin.

B. Choose the best answers

1. The graph of the curve r^2 sec 2 is symmetric about

a) x-axis b) y-axis c) origin d) none

  1. The period of the Fourier series extension of a function defined on the interval

0  x  is

a)  b) 2  c)  2 d)^  4

3. The graph of the equation r tan secis

a) a circle b) cardioid c) straight line d) spiral

  1. The function 

x x

x x f x sin 0

cos 0 ( ) is

a) an even function b) odd function c) both d) none

5. The graph of the equation r  2 sin tan is symmetric about

a) x-axis b) y-axis c) origin d) none

docsity.com

  1. The binomial expansion of ( 1  x^2 )^4 have a) 8 terms b) 4 terms c) none of the options d) 6 terms
  2. The sum of the series ... 2! 4! 6!

2 4 6    

e e e is

a) cos e b) cos x c) ex d)cos ex

  1. The region in plane satisfying the conditions 2  r  3 and 4

^ ^  is

a) a circular plate b) a ring c) a semi ring d) quarter ring

9. The point of intersection of the equations r  4  4 cos and r  6 is ( select any

two choices)

a) (6, 3

) b) (6,- 3

) c) (-6, 3

) d) (-6,- 3

10. In the Fourier series for f ( x ) x on    x , at x  the series converges

to

a)  b) 0 c)  d) 2 

C. Sketch the graph of the cuve r cos 2 .

Question # 2 Evaluate the indefinite integral as a power series. What is the radius of convergence?

Question # 3

Use Taylor series to show that ei^ ^^ cos  i sin

Question # 4 Find the Fourier series of the function defined in the interval described in the figure below.

Draw the graph of the Fourier series extension. What is the period of the Fourier series?

docsity.com