Match the graph of the function with the corresponding derivative graph. (Sheet)
What is 1. D
2. C
3. A
4. B
100
What is displacement?
What is net change from original position
100
use the SUMRECT program on your calculator to find LRAM MRAM & RRAM; use 6 rectangles. f(x)= e^(-x^2)
a=0 b=2
What is LRAM: 1.045
MRAM: 0.882
RRAM: 0.718
100
find the volume of the bounded area between y=x+3 and y=(x^2)+1 revolved around the x-axis. (see diagram on board)
What is 117π/5
200
determine whether the function is odd, even, or neither.
y= ___x^3___
x^2 -1
what is odd
200
find f'(x) f(x)=log_2(3x+1)
What is dy/dx=
___3_____
(3x+1)ln2
200
What does LIPET stand for?
What is Logs, Inverse trig, Polynomial, Exponential, Trig
200
use trapezpidal method to solve
6
∫(x^2+5)dx with 6 trapezoids
0
What is 103
200
find the volume of x=12(y^2 - y^3) about the x-axis
(see diagram on board)
What is 3.77
300
Suppose you deposite $800.00 in an account that pays 6.3% annual interest. How much money will you have 8 years later if the interest is compounded quarterly?
What is $1,319.07
300
implicit - find dy/dx for x^2+y^2=1
What is dy/dx = -x/y
300
which theorem is this:
b
∫f(x)dx=F(b)-F(a)
a
What is the first fundamental theorem of calculus
300
use substitution for ∫√(tanx)(sec^2x)dx
What is 2/3 (tanx)^(3/2) +C
300
find the area of the shaded region bounded by y=1, y=(x^2)/4, and y=x (see diagram on board)
What is 0.83
400
A rectangle box with a top has dimentions as shown (picture will be drawn on the board) and the perimeter of the right side is 50 inches. What are x and y, such that the box has the largest possible volume?
What is x=12.5 inches, y=12.5 inches
400
find dy/dx for x^3+y^3=18xy
What is dy/dx=
___x^2-6y___
6x-y^2
400
What is the value that would give the same area if the function was a constant? (hint ex: what is the height of a rectangle that would give you the same area?)
What is the average value of a function
400
use tabular method for ∫x^3(cos2x)dx
What is (answer on board)
400
find the area of the region in the first quadrant bouned by the lines y=x, x=2, y=1/(x^2), and the x-axis.
(see diagram on board)
What is 1.
500
use sandwich theorem to find:
lim(x→0) for (x^2)sinx
What is 0
500
use logarithmic differentiation to find dy/dx
√(x-3)^4(x^2+1)/ (2x+5)^3
(on board)
What is (answer on board)
500
What does this equation represent? (draw on board)
What is Riemann Sum
500
use integration by parts to solve ∫x^2(cosx)dx
What is (answer on board)
500
find the volume of the slabs. The base is the region between y=√x, y=0, and x=4. Cross sections perpendicular to the x-axis are semi-circles with the diameter across the base. (see diagram on board)