Math 5B Hybrid inal Exam all 2022
Please show all of your work. Each problem is worth 20 points for a total of 200
(unscaled) points.
In problems #1 and #2 differentiate with respect to x .
#1.) y = ( sin x )
cos x
Use logarithmic differentiation.
#2.) y = x3 Use logarithmic differentiation.
x
#3.) Find lim ( cos x )
1/ x 2
x ?0
#4.) Find lim ( 4 x + 1)
cot x
x ?0+
#5.) Evaluate ? t 3e?t dt
2
#6.) Evaluate ?
x2 ? 2 x ?1
( x ? 1) ( x 2 + 1)
2
dx
#7.) At what points on x = t 3 + 4t , y = 6t 2 is the tangent parallel to the line with
equations x = ?7t , y = 12t ? 5 .
?
1
.
n =1 2 + sin ( n )
#8.) Test the series for convergence or divergence: ?
?
#9.) Find the radius of convergence of the power series: ?
n =1
#10.) What is the Maclaurin series of f ( x ) = x cos x ?
n
n
8
( x + 6) .
n

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