exam2A - TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS MATH 251-510 Exam 2 version A, 11 Oct 2007 Name: Points: /60 In all questions no work = ⇒ no points! 1. True or false? Give explanations! (a) There is a function f such that f x = y sin( x ) and f y = cos( x ). (b) If f ( x, y ) = e x 2 then ∇ f = 2 xe x 2 . (c) If f ( x, y ) = e x 2 then df = 2 xe x 2 dx . (d) A drop of water placed in point p on a surface will go down in the direction −∇ f ( p ). (e) Range of f ( x, y ) = ln( x 2 + y 2 ) is { ( x, y ) : ( x, y ) negationslash = (0 , 0) } (all points apart from the origin). (10 points) 2. Below, “derivative” refers to the directional derivative. Give your answers with respect to the gradient ∇ f (in (a)-(c) just giving an answer is enough): (a) In which direction is the derivative of f maximal? (b) What is the maximal value of the derivative? (c) In which direction is the derivative of f minimal?...
View Full Document

{[ snackBarMessage ]}

Page1 / 7

exam2A - TEXAS A&M UNIVERSITY DEPARTMENT OF MATHEMATICS...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online