Exam 2 Calc - Version 004 Exam 2 gualdani (56410) 1 This...

Info iconThis preview shows pages 1–3. 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: Version 004 Exam 2 gualdani (56410) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine dy/dx when 6 cos x sin y = 1 . 1. dy dx = tan xy 2. dy dx = tan x 3. dy dx = cot x tan y 4. dy dx = cot x cot y 5. dy dx = tan x tan y correct Explanation: Differentiating implicitly with respect to x we see that 6 braceleftBig cos x cos y dy dx sin y sin x bracerightBig = 0 . Thus dy dx cos x cos y = sin x sin y . Consequently, dy dx = sin x sin y cos x cos y = tan x tan y . 002 10.0 points Find the slope of the tangent line to the graph of x 3 2 y 3 + xy = 0 at the point P (1 , 1). 1. slope = 5 4 2. slope = 3 2 3. slope = 4 5 correct 4. slope = 2 3 5. slope = 5 4 6. slope = 4 5 Explanation: Differentiating implicitly with respect to x we see that 3 x 2 6 y 2 dy dx + y + x dy dx = 0 . Consequently, dy dx = 3 x 2 + y 6 y 2 x . Hence at P (1 , 1) slope = dy dx vextendsingle vextendsingle vextendsingle P = 4 5 . 003 10.0 points Find the differential dy when y = 3 + sin x 5 sin x . 1. dy = 5 sin x (5 sin x ) 2 dx 2. dy = 3 cos x 5 sin x dx 3. dy = 3 sin x (5 sin x ) 2 dx 4. dy = 8 cos x (5 sin x ) 2 dx 5. dy = 8 cos x 5 sin x dx 6. dy = 8 cos x (5 sin x ) 2 dx correct Version 004 Exam 2 gualdani (56410) 2 Explanation: After differentiation of y = 3 + sin x 5 sin x using the quotient rule we see that dy = (5 sin x ) cos x + cos x (3 + sin x ) (5 sin x ) 2 dx . Consequently, dy = 8 cos x (5 sin x ) 2 dx . 004 10.0 points If f is the function whose graph is given by 2 4 6 2 4 6 which of the following properties does f have? A. local maximum at x = 4 , B. differentiable at x = 2 , C. f ( x ) > 0 on ( 1 , 2) . 1. none of them 2. C only 3. A and C only 4. all of them 5. A and B only 6. A only correct 7. B only 8. B and C only Explanation: The given graph has a removable disconti- nuity at x = 4 and a critical point at x = 2. On the other hand, recall that f has a local maximum at a point c when f ( x ) f ( c ) for all x near c . Thus f could have a local max- imum even if the graph of f has a removable discontinuity at c ; similarly, the definition of local minimum allows the graph of f to have a local minimum at a removable disconitu- ity. So it makes sense to ask if f has a local extremum at x = 4. Inspection of the graph now shows of the three properties A. f has , B. f does not have , C. f does not have . 005 10.0 points Find the absolute minimum value of f ( x ) = 1 + 2 cos 2 x on [ , ]. 1. abs minimum value = 1 correct 2. abs minimum value = 0 3. abs minimum value = 2 4. abs minimum value = 4 5. abs minimum value = 2 6. abs minimum value = 3 Explanation: The absolute minimum value of f on [ , ] occurs (a) either at an endpoint x = or x = , (b) or at a critical point of f in ( , ). Version 004 Exam 2 gualdani (56410)...
View Full Document

Page1 / 10

Exam 2 Calc - Version 004 Exam 2 gualdani (56410) 1 This...

This preview shows document pages 1 - 3. Sign up to view the full document.

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