Math 251 Quiz 6 October 23, 2009 Name:
Dierentiate the following functions.
1. f (t) =
2t
2+ t
Solution:
We use the Quotient Rule:
f (t) =
2. f () =
(2 +
t)2 2t(1/2)t1/2
(2 + t)2
sec
1 + sec
Solutio
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Mt. San J acinto College, Temecula Education Complex _ V . \:
Quiz 4 of Math 135 - 5145 . . .
April 7, 2016
Students Name:
Instructions: Show all your work for full credit. I
Mt. San Jacinto College, Temecula Education Complex
Quiz 2 of Math 135 5145
i-vhrlmry 25. 20 l 6
Students Name: _Snl_ulinn_
Instructions: Show all your work for full credit. lmlimu- your answers clear
Mt. San Jacinto College, Ternecula Education Complex
(TakaHome) Quiz 1 of Math 135 5145
February 11. 2016
Students Namei Sglukgn
Instructions: Show all your work for full credit. Indicate your answers
Analysis of Functions I
Increase, Decrease, and Concavity
Definition. Let f(x) be defined on an interval, and let x1 and x2
denote points in that interval.
(a) f is increasing on the interval if f(x1)
AB Calculus
Differentiability and Piecewise Functions
To determine if differentiable at the point of change, 3: = c I
Theorem:
If f (x) is continuous at x=c and lint f'(x) and lint f (x) exist.
i)C .
Differentiability
Piecewise functions may or may not be differentiable on
their domains.
To be differentiable at a point x = c , the function must be
continuous, and we will then see if it is differen
Mt. San J acinto College, Temecula Education Complex
Quiz 5 of Math 135 5145
May 5, 2016
Students Name: Sold-cfw_on
Instructions: Show all your work for full credit. Indicate your answers clearly.
Pro
Math 251 Exam 1 Oct. 2, 2009
Name
Directions
1. SHOW YOUR WORK and be thorough in your solutions. Partial credit will only be given for work
shown.
2. Any numerical answers should be left in exact for
Math 251 Exam 3 Dec. 2, 2009
SOLUTIONS
Directions
1. SHOW YOUR WORK and be thorough in your solutions. Partial credit will only be given for work
shown.
2. Any numerical answers should be left in exac
Math 251 Exam 2 Nov. 4, 2009
SOLUTIONS
Directions
1. SHOW YOUR WORK and be thorough in your solutions. Partial credit will only be given for work
shown.
2. Any numerical answers should be left in exac
Math 251 Quiz 7 Nov. 1, 2009 SOLUTIONS
1. Suppose that x and y are related by the following equation:
ey cos x = 1 + sin(xy)
Find
dy
dx
by implicit dierentiation.
Solution:
We dierentiate both sides w
Math 251 Quiz 5 October 16, 2009 Name:
1. Make a careful sketch of the graph of the function f (x) = sin x. On another set of axes, give a rough
sketch of the derivative f (x).
Solution:
1
2. Use the
Math 251 Quiz 4 October 7, 2009 Name: SOLUTIONS
1. The number of bacteria after t hours in a controlled laboratory experiment is n = f (t).
(a) What is the meaning of the derivative f (5)?
(b) Suppose
Math 251 Quiz 8 Nov. 13, 2009 SOLUTIONS
1. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley
on the dock that is 1 meter higher than the bow of the bo
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