{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Exam2_3 2 - Version 208 Exam 2 Radin(58305 Explanation...

This preview shows page 1. Sign up to view the full content.

Version 208 – Exam 2 – Radin – (58305) 2 Explanation: After implicit differentiation with respect to x we see that 2 xy cos( x 2 ) + y sin( x 2 ) = 0 . Consequently, dy dx = 2 xy cos( x 2 ) sin( x 2 ) = 2 xy cot( x 2 ) . 004 10.0 points Find an equation for the tangent line to the curve 6 x 2 + xy + 6 y 2 = 13 at the point (1 , 1). 1. y = x + 5 2. y = 3 x 4 3. y = 5 x + 2 4. y = 3 x + 2 5. y = 5 x + 2 6. y = x + 2 correct Explanation: Differentiating implicitly, we see that 6 x 2 + xy + 6 y 2 = 13 12 x + xy + y · 1 + 12 yy = 0 xy + 12 yy = 12 x y y ( x + 12 y ) = 12 x y y = 12 x y x + 12 y When x = 1 and y = 1, we have y = 12 1 1 + 12 = 13 13 = 1 so an equation of the tangent line is y 1 = 1 ( x 1) y = x + 2 keywords: 005 10.0 points If a tank holds 2000 gallons of water, and the water can drain from the tank in 40 min- utes, then Torricelli’s Law gives the volume V of water remaining in the tank after t minutes as V = 2000 parenleftbigg 1 t 40 parenrightbigg 2 . Find the rate at which water is draining from
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online