140 Final
Name
Show All the Work to Get Full Credit!
?
?
for x < 1?
?3?x
4
for x = 1
(30)1. Sketch the graph of the function f de?ned as follows: f (x) =
? 2
?
x + 1 for x > 1
Find limx?1? f (x), limx?1+ f (x), limx?1 f (x). Is the function continuous at x = 1?
(60)2. Find the limit.
x
1. limx?? (1/x)ln(ln(x))
2. limx??? 3?3
5?5x
3. limx?1+ ln(x5 ? 1) ? ln(x5 + 5)
4. limx?0 x2 cos(1/x2 )
(10) 3. Find the derivative DO NOT SIMPLIFY.
1. f (x) = cos(3×2 ) + cos2 (3x)
(10) 4. Use implicit di?erentiation to ?nd y ? .
1. y 2 = x cos y
(30) 5. According to the guidelines to graph f (x) = ln(sin x)
1. Find Domain of the function.
2. Find the horizontal asymptotes.
3. What is x-intercept and y-intercept.
4. Find the increasing and decreasing intervals, and local maximal or minimal value.
5. Find the concave up or concave down intervals, and inflection point.
6. Graph the function according to above information.
(30)6. Sketch the region and ?nd the area or the volume. ONLY SET UP and
DO NOT SOLVE.
1. Find the area under the curves x = y 2 , y ? x = 2, y = ?2, y = 3.
2. Find the volume by disk of the region bounded by y = ex , y = x, x = 0, x = 1 revolved
about x-axis.
3. Find the volume by shell of the region bounded by y = x, y = 1, x = 0 revolved about
the line y = 1.
(30)7. Evaluate.
?8
3
1. ?1 ?x+1
dx
2.
3.
?
tan xdx
? 2 tan?1 (?x) tan2 x
dx
?2
1 + x2
1

Purchase answer to see full
attachment