IPS 1500 Math Problem Set 3
Fall 2015: Due Friday Oct. 2nd in class.
Problems must be turned in on paper.
Directions: The problems below have detailed directions. Failure to follow the directions will be
penalized. Even if the directions do not require yo
IPS 1500 Math Problem Set 2
Fall 2015: Due Friday Sept. 25th in class.
Problems must be turned in on paper.
Directions: The problems below have detailed directions. Failure to follow the directions will be
penalized. Even if the directions do not require
IPS 1500 Math Problem KEY 1
Fall 2015
Problem 1 *10 pts
Solve the equation x2 x 1 = 0 by completing the square and then solve it again using the quadratic
formula. Show all of your work, neatly, for both parts of the problem. State explicitly the values o
Tuesday Quiz
Explain, in grammatical English sentences, where the function
f (x) = Cos(1 x2 )
is continuous and why. You should reference the rules for continuity given in class.
Key:
The function 1 x2 is a polynomial and so is continuous everywhere. We a
Tuesday Quiz
Find the value c specied by the mean value theorem where the slope of the tangent line to
f (x) = x3 4x
has the same slope as the secant line from the point where x=0 to the point where x=3.
Key:
The secant runs from (0,0) to (3,15) and so ha
Tuesday Quiz
Use the cross product to nd a vector at right angles to both (1,1,1) and (-1,0,1) and then use
the dot product to verify your answer against both the vectors above.
Key:
Cross product:
(1, 1, 1) (1, 0, 1) = (1, 2, 1)
Verify:
(1, 1, 1) (1, 2,
Tuesday Quiz
Compute:
x Cos(x) dx
Key:
Use parts with U = x, dV = Cos(x) dx. Then dU = dx and V = Sin(x)
U dV = U V
V dU
x Cos(x) dx = x Sin(x)
Sin(x) dx
= x Sin(x) + Cos(x) + C
1
Friday Quiz
Compute:
x2 dx
x3 + 5
Key:
1
Let u = x3 + 5, then 3 du = x2 d
Where is f (x) =
x
x2 4
Tuesday Quiz
decreasing? Give your answer as a range of values.
Key:
f (x) =
(x2 4)(1) x(2x)
x2 + 4
= 2
(x2 4)2
(x 4)2
So the critical points are x = 2 (the vertical asymptotes). Then the sign chart looks like:
() (2) (2) (+)
and w
Tuesday Quiz
x
If f (x) = Sin(e ) what is f (x)?
Key:
Using the chain rule, f (x) = Cos(ex ) ex .
1
Friday Quiz
Sin(x)
If f (x) = e
what is f (x)?
Key:
Using the chain rule, f (x) = eSin(x) Cos(x)
2
Tuesday Quiz
Suppose that tted womens t-shirts cost ve dollars more then mens t-shirts. Suppose the
math-stat club has eleven female members and nine male members. If the bill to get t-shirts for
everyone is $215 then nd and report the cost of each sort o