Misc
L'Hopital's Rule
Optimization
Indefinite Integrals
Definite Integrals
100
What is the difference between mean value theorem and rolle's theorem?
Rolles requires F(a)=F(b)
100
What are the two indeterminate forms we can use L'hopitals rule for?
0/0, inf/inf
100
What two equations do we need to complete an optimization problem?
Constraint, objective
100
Why do we put the +C on an antiderivative?
General solution
100
In reimann sum thing if you are doing 10 sub intervals from 0 to 4 then what is your delta x?
4/10
200
Approximate (8.05)^1/3
2.004
200
Find the limit as x goes to infinity of (x^2-3x)/(x^3+3)
0
200
If we have a closed interval, what are the 3 methods we can use to check to see if our value is either a max or min?
1st Derivative Test 2nd Derivative Test Plug in each end point
200
Find the antiderivative of sec(x)^2-cos(x)+3
tan(x)-sin(x)+3x+C
200
Evaluate the integral from 0 to 4 of x^2+4
112/3
300
Who is a sorry receiver that Richard Sherman doesn't like?
Crabtree!
300
When using L'Hopital's rule, what symbol must be used?
L over the equal sign
300
Find two positive numbers whose product is 100 and whose sum is a minimum.
10,10
300
Find F(x) if f(x)=x^1/2+7x-3
2/3*x^3/2+7/2*x^2-3x+c
300
Evalaute the integral from 5 to 5 of csc^2(x^9)*3x-tan(x)
0
400
If g(x)= the integral from 0 to x^2 of 2-t then find g'(x)
4x-2x^3
400
Find the limit as x approaches 4 of (x^2-16)/(x-4)
8
400
An open-top rectangular box is constructed from a 10 in. by 16 in. piece of cardboard by cutting squares of equal side length from the corners and folding up the sides. Find the dimensions of the box of largest volume. Give the maximum volume also.
2*6*12 V=144
400
True or false and explain why: If f(x)=x^2 and F(x)=x^3/3 then F(x) is the general antiderivative of f
False, it is the specific antiderivative when c=0
400
Evaluate the integral from -5 to 10 of (x^5-2x^2+7)/x^4
38079/1000
500
Using a right reimann sum evaluate the integral from 0 to 1 of 2x.
1
500
limit as x goes to infinity of (x-(x^2+x)^1/2)
-1/2
500
Mr. Guest decides to quit teaching and instead work at the post office. Unfortunately, he is lousy at his new job and gets demoted to the box cutter division. His boss tells him that he must make a box whose base is 3 times longer than the width of the box. If the box volume has to be 50 cubic feet then what are the minimum dimensions for the sides of the box?
w=(20/3)^1/3=1.88 l=3*w=5.64 h=4.7
500
find F(x) if f(x)=(x^3-x^2+1)/x^2
1/2*x^2-x-1/x+C
500
Evaluate the integral from 0 to Pi of cos(x)^-2*sin(x)
-2
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