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Honors Calculus II [2423-001] Midterm II
Q1].[20 points] Evaluate the following expressions and limits. Since you dont have a calculator, square roots,
fractions etc. are allowed in your answers.
log2 ( 1 )
8
Answer: Since 1/8 = 81
Q1]. . . [13 points] Use logarithmic dierentiation to compute the derivative f (x) of the following function
f (x) = x
x
Take logs of the equation y = x x to get ln y = ln(x x ) = x ln(x). Dierentiate this expression with
respect to x to get
1
1
ln(x) +
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Honors Calculus II [2423-001] Midterm I
For full credit, please show all your work.
Q1].[12 points] Evaluate the following limit of Riemann sums by rst converting to a denite integral,
and then evaluating the integral.
n
1
i
lim
1+
Trigonometry Review
Although you probably know enough about trigonometry to get by in this class already, it might make
the class a lot easier for you if you take a little time to brush up on the following basic facts. Theyre taken
from Appendix D of the
Review sheet for 3rd exam
The third exam will cover sections 7.4, 7.6, 7.8, 8.1, 8.2 and 8.3. You should review the problems from
Assignments 8, 9, 10, and 11; and Quizzes 5 and 6. I recommend trying to do similar problems (you can
easily recognize which
Review for Exam 2
This exam covers sections 6.2, 6.3, 6.4, 7.2, 7.3, and 7.4 of the text.
d
dx
It will include a question asking you to prove one or more of the following formulas: (i)
1
d
1
d
1
ln x = x ; (iii) dx arcsin x = 1x2 ; or (iv) dx arctan x = 1
Review for Test 1
This test is over the material in Sections 5.1, 5.2, 5.3, 5.4, 5.5, and 6.1 of the text,
which was covered in Assignments 1, 2, and 3. In addition to going over the homework
problems from these assignments to make sure you understand how
Homework 14 Solutions
7.8 #2. (a) proper, (b) Type 2, because it has discontinuity at
x = /2, (c) Type 2, because it has discontinuity at x = 1, (d) Type
1, because the interval of integration is innite.
7.8 #10. The integral is improper because the inter