Math 51 Practice Midterm 1 - Version C
Math 51, Prof. Ohm
Practice Midterm 1 - Version C
Name:
Student ID:
1. You have 50 minutes to complete this exam.
2. Write your name on every page.
3. There are 5 questions in this exam.
4. The exam is closed book. No calculators or cheat sheets are allowed.
5. Cell phones or any other electronic devices are not allowed on desktops.
6. Please do not submit extra sheets, as they will not be graded.
7. All work must be your individual efforts.
8. Always justify your answers and show all your work. Write your answers and
all accompanying work neatly. Simplify your answers.
These practice exams are copyrighted and may not be redistributed without 1
written permission from the UC Berkeley Department of Mathematics.
Math 51 Practice Midterm 1 - Version C
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written permission from the UC Berkeley Department of Mathematics.
Math 51 Practice Midterm 1 - Version C
Name :
1. Consider the functions
1
f (x) = and g(x) = log3 (10 − x)
x−2
(a) Find (f ◦ g)(x).
(b) Find the domain of (f ◦ g)(x).
These practice exams are copyrighted and may not be redistributed without 3
written permission from the UC Berkeley Department of Mathematics.
Math 51 Practice Midterm 1 - Version C
2. Calculate the following limits. If a limit does not exist, determine if it is ∞, -∞, or
neither.
9 − x2
(a) lim .
x→3 x2 − 8x + 15
1
(b) lim arctan( ).
x→0 x
These practice exams are copyrighted and may not be redistributed without 4
written permission from the UC Berkeley Department of Mathematics.
Math 51 Practice Midterm 1 - Version C
Name :
3. Let (
et−1 − 2t + 5 if t < 1
f (t) = .
log3 tc if t ≥ 1
Find the value of c such that limx→1 f (t) exists.
These practice exams are copyrighted and may not be redistributed without 5
written permission from the UC Berkeley Department of Mathematics.
Math 51 Practice Midterm 1 - Version C
4. (a) Find the value arcsin sin( 4π
3
) .
(b) Simplify the expression sin arctan(x2 ) in terms of x.
These practice exams are copyrighted and may not be redistributed without 6
written permission from the UC Berkeley Department of Mathematics.
Math 51 Practice Midterm 1 - Version C
Name :
5. Explain why the equation ex = cos x + 1 must have a solution in the interval (0, 2).
These practice exams are copyrighted and may not be redistributed without 7
written permission from the UC Berkeley Department of Mathematics.
Math 51 Practice Midterm 1 - Version C
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These practice exams are copyrighted and may not be redistributed without 8
written permission from the UC Berkeley Department of Mathematics.
