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
Solution:
We again use the Quotient Rule, noting that the deri
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 clearly.
Problem 1. (7 pts) Find the dcrivnliw of the functi
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 clearly.
Problem 1. [ml
1'2 "21
I") 1-1 4x+4
(n) (6
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) < f(x2) whenever x1< x2.
(b) f is decreasing on the in
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 . x>c
Then f is differentiable at x = c: if these limits
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 differentiable.
Lets consider some piecewise functions first.
L
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.
Problem. (5 pts each) Evaluate each of the following denit
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 form, i.e, no decimal approximations.
3. You may use calcu
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 exact form, i.e, no decimal approximations.
3. You may use
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 exact form, i.e, no decimal approximations.
3. You may use
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 with respect to x, treating y as a function of x:
dy
dy
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 denition of the derivative (i.e., use the h limit) to n
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 there is an unlimited amount of space and nutrients fo
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 boat. If the rope is pulled in at a rate of 1 m/s,
how fa
- V . o. a"! "25' 3. -'
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. Indicate your answers clearly. ' _ -
Problem. Graph the