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

Mathematics Exam: Limits, Gradients, and Integrals, Exams of Calculus

All India Institute of Medical SciencesCalculus

A mathematics exam focusing on limits, gradients, and integrals. The exam consists of 7 problems, including finding limits, computing gradients, and evaluating integrals. Students are required to write their names and ids, and are given 150 minutes to complete the exam.

Typology: Exams

2012/2013

Uploaded on 02/25/2013

ekana
ekana 🇮🇳

4

(44)

370 documents

1 / 19

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Final 253
You have 150 min to solve 7 problems. Please note
•Write your name/student id clearly
•Write only on one side of the paper in the space design for it. Use the last
few pages of the exam for calculations.
Good luck!
Name: xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Student ID: xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
1
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13

Partial preview of the text

Download Mathematics Exam: Limits, Gradients, and Integrals and more Exams Calculus in PDF only on Docsity!

Good luck!^ •^ • Final 253^ You have 150 min to solve 7 problems. Please note Name: Student ID:^ Write your name/student id clearlyWrite only on one side of the paper in the space design for it. Use the lastfew pages of the exam for calculations. xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

  1. (a) Compute the gradient of the function (b) Use the gradient to approximate f (x, y f ) =(0, 0 ∫.1). (^) xy cos(t (^2) ) dt
  1. Find the direction in which the directional derivative of the function at point (0, 2) has the value 1. f (x, y) = ye−xy
    1. Find the limit or show that it does not exist (x,y,zlim)→(0, 0 ,0) xy x 2 + + yz y 22 ++ zxz
    1. If(a)(b) z = f (x, y) where x = s + t and4(( zyzx x=) 2 )( s−z y− ) = ((z ty )show that 2 z= (s) 2 z−s) ( (zztt))
    1. a Find the critical points of the function b Explore the points and check if they are minima/maxima or saddle pointsc In 3 lines or less, explain why the result you obtain does not have an equivalentwhen considering a function of a single variable. f (x, y) = −(x 2 − 1) 2 − (x 2 y − x − 1)
    1. Evaluate the integral where D is the domain enclosed by the lines x − 2 y = 0, x − 2 Iy == 4 ∫ ∫, D 3 x 3 x x− −− 2 yyy = 1dA and 3 x − y =

Scrap Paper (we will not look here)

Scrap Paper (we will not look here)

Scrap Paper (we will not look here)