CUNY Lehman College Algebra Worksheet

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Math181 Midterm-MorningA.pdf
00.
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(3x – 5,
4. lim f(x), where f(x) =
(x3 – 5x + 2, x> 1
x 51
X-4
5. Consider the function f(x) =
x2 + 3x-28
a. Find any values of x for which the function is discontinuous.
b. Classify each of the function’s discontinuities as removable, jump, or infinite.
6. Find the derivative of f(x) = x2 + 3x – 5 using the limit definition of the derivative.
7. Find the derivative of g(x) = (2xVx.
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Math181 Midterm-MorningA.pdf
000
he derivative of f(x) = x2 + 3x – 5 using the limit definition of the derivative.
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7. Find the derivative of g(x) = (2xVx.
x2-4
8. Find the derivative of h(x) =
2x+1
9. Find the derivative of f(x) = Vx2 + 5x.
10. Find the equation of the line tangent to the graph of y = cos
when x = 21.
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Math181 Midterm-MorningA.pdf
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9. Find the derivative of f(x) = Vx2 + 5x.
10. Find the equation of the line tangent to the graph of y = cos
when x = 21.
11. Find the derivative of g(x) = x3 sin-x.
12. Find the equation of the tangent line to the curve given by 2×2 + y3 = 5y + 3x at the
point (2,2).
13. Find the derivative of f(x) = x2x-7
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Math181 Midterm-MorningA.pdf
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Name:
Math 181 Midterm Exam – Morning Version A
Directions: Answer each of the following questions, showing all work needed to reach the
solution. Answers must be in exact form (in terms of t, radicals, e, etc.) unless otherwise
noted. When you are finished, scan and submit your work on Blackboard no later than
12:05pm – late submissions will not be accepted.
Good luck!
For each of the problems #1-4, either evaluate the limit or explain why it does not exist.
1. lim (V)
4
x2 +8x+15
2. lim
—3×2+x-6
3. lim 2013
X-2 X-2
4. lim f(x), where f(x) = { 1 = 5x +2, +31
(3x – ,
XS1
X-4
5. Consider the function f(x) =
x2+3x-28
a. Find any values of x for which the function is discontinuous.
b. Classify each of the function’s discontinuities as removable, jump, or infinite.