MATH 151 Midterm: MATH 151 TAMU Y2009 2009a Exam 2b
MATH 151, SPRING SEMESTER 2009
COMMON EXAMINATION II - VERSION B
Name (print):
Signature:
Instructor’s name:
Section No:
INSTRUCTIONS
1. In Part 1 (Problems 1–11), mark your responses on your ScanTron form using a No:
2 pencil. For your own record, mark your choices on the exam as well. Collected
scantrons will not be returned after the examination.
2. Calculators should not be used throughout the examination.
3. In Part 2 (Problems 12–16), present your solutions in the space provided. Show all
your work neatly and concisely, and indicate your final answer clearly. You will
be graded, not merely on the final answer, but also on the quality and correctness of
the work leading up to it.
4. Be sure to write your name, section number, and version letter of the exam
on the ScanTron form.
1
Part 1 – Multiple Choice (44 points)
Each question is worth 4 points. Mark your responses on the ScanTron form and on the
exam itself .
1. Differentiate the function 2 cos x−sin xwith respect to x.
(a) −2 sin x−cos x
(b) 2 cos x+ sin x
(c) −2 cos x+ sin x
(d) −2 sin x+ cos x
(e) 2 cos x−sin x
2. Compute the slope of the tangent to the curve y=x−sec xat the point (0,−1).
(a) −1
(b) 1
(c) −2
(d) 2
(e) 0
3. Given that f(x) = (3x−1)8, find the value of f′(0).
(a) −24
(b) −16
(c) −8
(d) 16
(e) 24
2
4. Compute the 11th derivative of f(x) = sin xwith respect to x.
(a) sin x+ cos x
(b) −sin x
(c) sin x
(d) cos x
(e) −cos x
5. Determine the tangent vector to the vector function r(t) = ht1/3, e2ti, corresponding
to t= 1.
(a) h2e2,1/3i
(b) h1/3, e2i
(c) he2,1/3i
(d) h1/3,2e2i
(e) h1,1i
6. Suppose that one begins to solve the equation x3−2x−5 = 0 using Newton’s method.
If x1is chosen to be 2, what is x2?
(a) 5/2
(b) 19/10
(c) 21/10
(d) 9/4
(e) 7/3
3
Document Summary
Instructions: in part 1 (problems 1 11), mark your responses on your scantron form using a no: For your own record, mark your choices on the exam as well. Collected scantrons will not be returned after the examination: calculators should not be used throughout the examination, in part 2 (problems 12 16), present your solutions in the space provided. If x1 is chosen to be 2, what is x2? (a) 5/2 (b) 19/10 (c) 21/10 (d) 9/4 (e) 7/3. 2 + 3(1/x) . (a) 1/2 (b) 2 (c) 2 (d) 1/2 (e) 0: consider the functions f1(x) = x2, f2(x) = cos(x), and f3(x) = sin(x). 1 + x2 can be shown to be one-to-one on the interval [0, ). Determine f 1 (the inverse of f ), and state its domain. (a) f 1(x) = r 1 2x x. 1 2x (b) f 1(x) = x domain=(0, 1/2] domain=(0, ) (c) f 1(x) = r 2 x x.
