Exam2_3 2 - Version 208 – Exam 2 – Radin – (58305)...

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

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: Version 208 – Exam 2 – Radin – (58305) Explanation: After implicit differentiation with respect to x we see that 2xy cos(x2 ) + y ′ sin(x2 ) = 0 . Consequently, dy 2xy cos(x2 ) =− = −2xy cot(x2 ) . dx sin(x2 ) 004 10.0 points Find an equation for the tangent line to the curve 6x2 + xy + 6y 2 = 13 at the point (1, 1). 1. y = x + 5 2. y = 3x − 4 3. y = 5x + 2 4. y = −3x + 2 5. y = −5x + 2 6. y = −x + 2 correct Explanation: Differentiating implicitly, we see that 6x2 + xy + 6y 2 = 13 12x + xy ′ + y · 1 + 12yy ′ = 0 xy ′ + 12yy ′ = −12x − y y ′ (x + 12y ) = −12x − y −12x − y y′ = x + 12y When x = 1 and y = 1, we have y′ = −13 −12 − 1 = = −1 1 + 12 13 so an equation of the tangent line is y − 1 = −1 (x − 1) y = −x + 2 2 keywords: 10.0 points 005 If a tank holds 2000 gallons of water, and the water can drain from the tank in 40 minutes, then Torricelli’s Law gives the volume V of water remaining in the tank after t minutes as 2 t V = 2000 1 − . 40 Find the rate at which water is draining from the tank after 30 minutes. 1. rate = 27 gal/min 2. rate = 20 gal/min 3. rate = 22 gal/min 4. rate = 21 gal/min 5. rate = 25 gal/min correct Explanation: By the Chain Rule, 1 2000 1− t 20 40 1 = −100 1 − t , 40 V ′ ( t) = − the negative sign indicating that the volume is decreasing. Consequently, after 30 minutes the water is draining from the tank at a rate = 100 1 − 006 30 40 = 25 gal/min . 10.0 points A 15 foot ladder is leaning against a wall. If the foot of the ladder is sliding away from the wall at a rate of 5 ft/sec, at what speed is the top of the ladder falling when the foot of ...
View Full Document

Ask a homework question - tutors are online