Exam_2_20C_Solution

Exam_2_20C_Solution - Math 20C Summer 2010 Exam 2 Solution...

Info iconThis preview shows pages 1–2. 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: Math 20C. Summer, 2010. Exam 2 Solution. 1. The radius of the circle is √ 4 = 2 meters. • Since the object is moving counterclockwise, κ = 1 2 meter − 1 • T = < − 1 , > • N = < , − 1 > • a = s ′′ T + κ ( s ′ ) 2 N • < 5 , − 8 > = s ′′ < − 1 , > + 1 2 ( s ′ ) 2 < , − 1 > = < s ′′ , − 1 2 ( s ′ ) 2 > • s ′′ = − 5 • 1 2 ( s ′ ) 2 = 8 • ( s ′ ) 2 = 16 • s ′ = 4. The object is traveling 4 meters per second and is slowing down 5 meters per second 2 2. f ( x,y ) = 2 x − y + 6 • f = c ⇐⇒ 2 x − y + 6 = c ⇐⇒ y = 2 x + 6 − c • f = 4 on y = 2 x + 2 • f = 6 on y = 2 x • f = 8 on y = 2 x − 2 • f x = ∂ ∂x (2 x − y +6) = 2 • f y = ∂ ∂y (2 x − y +6) = − 1 • ∇ f = ( 2 , − 1 ) • Figure A3 4 6 8 x 2 y 1 ∇ f Figure A3 3. V = πr 2 h • V r = 2 πrh • V h = πr 2 • V (3 , 2) = π (3 2 )(2) = 18 π • V r (3 , 2) = 2 π (3)(2) = 12 π • V h (3 , 2) = π (3 2 ) = 9 π • Tangent plane:...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

Exam_2_20C_Solution - Math 20C Summer 2010 Exam 2 Solution...

This preview shows document pages 1 - 2. Sign up to view the full document.

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