math226spring08mt1s

math226spring08mt1s - 1 . a) The sun is melting a...

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 DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 . a) The sun is melting a rectangular block of ice. When the blocks height x is 1 ft and the edge y of its square base is 2 ft, its height is decreasing at the 2 in./h and its base edge is decreasing at 3 in./h. What is the blocks rate of change of volume V = xy 2 at that instant? Answer. By chain rule, dV dt = V x dx dt + V y dy dt = y 2 dx dt + 2 xy dy dt = 2 2 (- 2 12 ) + 2 1 2 (- 3 12 ) =- 5 3 ( ft 3 /h ) . b) Determine the set of points at which the function is continuous: f ( x,y ) = xy x 2 +2 y 2 , if ( x,y ) 6 = (0 , 0) , 1 3 , if ( x,y ) = (0 , 0) . Answer . The function is continuous for ( x,y ) 6 = (0 , 0), as a quotient of two continuous functions (denominator nonzero). The value of f along the line y =- x is- x 2 3 x 2 =- 1 3 , therefore it is not continuous at (0 , 0) . The set of continuity are all ( x,y ) 6 = (0 , 0) . 2. a) Find the linearization of z = f ( x,y ) = xe- 2 y at (1 , 0). Approximate f (1 . 1 ,- . 1). Write the equation of the tangent plane to1)....
View Full Document

Page1 / 3

math226spring08mt1s - 1 . a) The sun is melting a...

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