1024worksheet8

1024worksheet8 - horizontal. (a) y = sin 2 x (b) y = tan...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Polytechnic Institute of NYU MA 1024/1324 Worksheet 8 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total 100 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
2 (1) Find the derivatives of the given functions. (a) y = cos 4 ( x ) (b) y = tan (cos x ) (c) y = tan ( x ) · e sin( x 2 ) (d) y = sin 2 (2 x ) + 2 cos 3 (3 x ) + 3
Background image of page 2
3 (2) Find the derivatives of the given functions. (a) y = p (cos(3 x )) 3 (b) y = tan x 2 + e 2 x (c) y = sin 2 x + sin ( x 2 ) (d) y = cos 4 (4 x ) · sin 7 (7 x )
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 (3) Verify the following differentiation formulas. (a) d dx (cot x ) = - csc 2 x (Hint: cot x = cos x sin x ) (b) d dx (sec x ) = sec x tan x (Hint: sec x = 1 cos x ) (c) d dx (csc x ) = - csc x cot x (Hint: csc x = 1 sin x )
Background image of page 4
5 (4) Find an equation for the tangent line to the curve at x = a . (a) y = csc x ; a = π/ 3 (b) y = tan x ; a = π/ 6 (c) y = cot x ; a = π/ 6
Background image of page 5

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

View Full DocumentRight Arrow Icon
6 (5) An object moves along the x -axis, its position at each time t being given by x ( t ). Determine those times from t = 0 to t = 2 π when the object is moving to the right ( x 0 ( t ) > 0) with increasing speed ( x 00 ( t ) > 0). (a) x ( t ) = sin t + cos t (b) x ( t ) = t - 2 sin t
Background image of page 6
7 (6) Determine the number x between 0 and 2 π where the tangent line to the curve is
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

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

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: horizontal. (a) y = sin 2 x (b) y = tan x-2 x (c) y = cot x-2 csc x 8 (7) Let f ( x ) = cos x, x ≥ ax + b, x < (a) Determine a and b so that f is differentiable at 0. (b) Using the values found above, sketch the graph of f . 9 (8) Let f ( x ) = sin x, x ≤ 2 π/ 3 ax + b, x > 2 π/ 3 (a) Determine a and b so that f is differentiable at 2 π/ 3. (b) Using the values found above, sketch the graph of f . 10 (9) Let f ( x ) = 1 + a cos x, x ≤ π/ 3 b + sin ± x 2 ² , x > π/ 3 (a) Determine a and b so that f is differentiable at π/ 3. (b) Using the values found above, sketch the graph of f . 11 (10) Let y = A sin ( ωt ) + B cos ( ωt ), where A , B , and ω are constants. Show that y satisfies the equation d 2 y dt 2 + ω 2 y = 0...
View Full Document

This note was uploaded on 12/09/2009 for the course MA 1024/1324 taught by Professor N/a during the Spring '09 term at NYU Poly.

Page1 / 11

1024worksheet8 - horizontal. (a) y = sin 2 x (b) y = tan...

This preview shows document pages 1 - 11. Sign up to view the full document.

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