MTH132-Test2 - a height m 10 and a base radius of m 4 ....

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Page 1 10/18/2011 Name (Print Clearly): Student Number: Oct 10, 2008 Instructor: Dr. W. Wu Instructions: Answer the following questions in the space provided. There is more than adequate space provided to answer each question. The total time allowed for this quiz is 50 minutes. 1 [5 pts each] . Find dx dy / of each of the following functions. Do Not Simplify (a) x y - = 3 (b) 4 ) 3 4 ( + = x y (c) 1 ) cot (csc - + = x x y (d) x x x x y 3 5 cos 3 sin 1 - = -
Background image of page 1

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

View Full DocumentRight Arrow Icon
Page 2 10/18/2011 (e) 1 1 2 2 + + + = x x x y (f) x y xy x 2 3 4 3 / 4 3 = - + (use implicit differentiation) 2 [5 pts each] . Let 1 2 1 ) ( + = x x f . (a) Find the derivative using the definition. (b) Find the derivative using differentiation rules.
Background image of page 2
Page 3 10/18/2011 3 [10 pts] . Show that ) 1 , 1 ( - lies on the curve y x y y x + = + 2 3 3 . Then find an equation for the tangent line to the curve at this point. 4 [10 pts] . Water drains from a conical tank at the rate of min / 5 3 m . The tank stands point down and has
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a height m 10 and a base radius of m 4 . Suppose the water is m 6 deep at this moment. (a) What is the relation between radius of the surface and the depth of the water? (b) What is the relation between the volume and depth of the water? (c) How fast is the water level dropping at this moment? Page 4 10/18/2011 5. [10 pts] . Let 5 . sin 1 ) (-+ + = x x x f (a) Find the linearization of ) ( x f at = x . (b) Estimate ) 1 . ( f using the result of (a). 6. [4 pts bonus]. When a tanker collides with a boat, 100 3 m of oil is spilled in the ocean. The resulting oil slick forms a right circular cylinder on the surface of the water. If the thickness of the slick is decreasing at a rate of sec / 001 . m , how fast is the radius increasing when the slick is m 01 . thick?...
View Full Document

Page1 / 4

MTH132-Test2 - a height m 10 and a base radius of m 4 ....

This preview shows document pages 1 - 4. Sign up to view the full document.

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