102-2006&amp;2007-2-F11-June2006

# 102-2006&amp;2007-2-F11-June2006 - Math 102 Calculus II...

This preview shows pages 1–2. Sign up to view the full content.

102, Calculus II Final Exam. Date: 01/06/2006 Duration: 2 hours. Answer all questions. Calculators and Mobile Phones are not allowed. 1. (4pts.) (a) Find the exact value of sin(tan-I(~)). (b) Find the exact value of coth(ln 2). 2. (4pts.) Let f(x) = fox tan(t) sec2(t)dt,O < x < 11/2. Find (a) f'(x) (b) f(1I/4) (c) (f-IY(~). 3. (12pts.) Find, if possible, (a) / tan~l x dx (b) jIlnx dx OJi 2 X (c) h ~ ~ d.'L 4. (4pts.) A curve C is given parametrically by x = (t2 + l)et and y (t3 + 2t2)et. (a) Find the points P (.'L, y) where the tangent is vertical. (b) Determine whether.C is concaveypw!1rds. or downwards at t .0. J. (4pts.) Find the area of the surface obtained by rotating the curve y = Jx + 1, 1 < x < 5 about the x-axis. 6. (4pts.) Find the centroid (center of mass) of the region bounded by the . 0 'if d 3 'if curves y = SIn x, y = , x = "4an x = 4' 7. (4pts.) Find the length of the curve T = 4 cos2(~). 8. (4pts.)

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

102-2006&amp;2007-2-F11-June2006 - Math 102 Calculus II...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online