Rate of Change of Function - Multivariable Calculus - Past Paper, Exams for Calculus. Agra University

Calculus

Description: These are the notes of Past Paper of Multivariable Calculus. Key important points are: Rate of Change of Function, Trigonometric Identities, Spherical Coordinates, Approximate Value, Numerical Values of Derivatives, Critical Points of Function, Tangent Plane
Showing pages  1  -  2  of  10
Name:
Lab Section:
MATH 215 – Fall 2004
FINAL EXAM
Show your work in this booklet.
Do NOT submit loose sheets of paper–They won’t be graded
Problem Points Score
1 15
2 10
3 25
4 10
5 15
6 15
7 10
TOTAL 100
Some useful trigonometric identities:
sin2θ+ cos2θ= 1 cos 2θ= cos2θsin2θsin 2θ= 2 sin θcos θ
sin2θ=1cos 2θ
2cos2θ=1 + cos 2θ
2
Spherical coordinates:
x=ρcos(θ) sin(φ)y=ρsin(θ) sin(φ)z=ρcos(φ)
1
Problem 1. (15 points) This problem is about the function
f(x, y, z) = 3zy + 4xcos(z).
(a) What is the rate of change of the function of fat (1,1,0) in the direction from this point to
the origin?
(b) Give an approximate value of f(0.9,1.2,0.11).
CONTINUED ON THE NEXT PAGE
2
The preview of this document ends here! Please or to read the full document or to download it.
Document information
Embed this document:
Docsity is not optimized for the browser you're using. In order to have a better experience please switch to Google Chrome, Firefox, Internet Explorer 9+ or Safari! Download Google Chrome