Graphing Trig Functions
Trig Equations
Sequences & Series
Intro to Calc
Misc.
100
What is the amplitude of
f(x)=-3sin(2x-pi)+2
3
100
Solve on the interval from [0,2pi]
5sinx=3sinx+sqrt3
x=pi/3 and (2pi)/3
100
Does the geometric series converge or diverge?
2-3+9/2-27/4...
Diverge
100
lim_(x->-oo)f(x)=(2x^2+4)/(3x^2)
2/3
100
Fill in the blanks: f(x) has a relative minimum of ____ which occurs at ____
f(x) has a relative minimum of -2 which occurs at 0
200
What is the phase shift of
f(x)=-sin(x+pi/4)
-pi/4
200
Solve on the interval from [0,2pi]
tanxcosx=tanx
x=0, pi, 2pi
200
Write the simplified expression for the nth term of the sequence:
7, 10, 13, 16,...
A_n=3n+4
200
Use the graph to find the limit of the following:
lim_(x->-oo)f(x)=
lim_(x->1)f(x)=
lim_(x->oo)f(x)=
lim_(x->-oo)f(x)=oo
lim_(x->1)f(x)=DNE
lim_(x->oo)f(x)=2
200
lim_(x->4)(x^2-16)/(x-4)
8
300
What is the domain & range of:
f(x)=4cos(pix)-1
Domain: All real numbers
Range: [-5,3]
300
Solve on the interval from [0,2pi]
2sin^2x=4sinx+6
x=(3pi)/2
300
Find the sum of the first 10 terms of the series:
243+81+27+9+...
Write your answer as a fraction
S_10=29524/81
300
Determine if f(x) is continuous at x=-3
Not continuous, the limit does not exist
300
Using the definition of continuity to explain why the graph is or is not continuous at x=-1
f(-1)=0
lim_(x->-1)f(x)=2
f(-1)!=lim_(x->-1)f(x) so the f(x) is not continuous at x=-1
400
Determine the amplitude, period, phase shift, and midline of
f(x)=-cos(2x-4pi)+2
Amplitude: 1
Period: pi
Phase Shift: 2pi
Midline: y=2
400
Solve on the interval from [0,2pi]
sin2x=cosx
x=pi/2,(3pi)/2, pi/6, (5pi)/6
400
An exhibit at a science museum offers visitors the opportunity to experiment with the motion of an object on a spring. One visitor pulled the object down and let it go. The object traveled a distance of four feet upward before heading back the other way. Each time the object changed direction, it moved only 75% as far as it did in the previous direction. If the spring was left to toggle back and forth infinitely, find the total distance the object traveled.
16 feet
400
Find the derivative of
f(x)=5x^2-x
f'(x)=10x-1
400
Expand: 3(x-h)^3
3x^3-9x^(2)h+9xh^2-h^3
500
Graph one cycle of:
f(x)=3cos(x+pi)-1
500
Solve on the interval from [0,2pi]
x=(7pi)/6,(11pi)/6
x=(7pi)/6,(11pi)/6
500
Write in sigma notation and find the sum of the first ten terms:
1/2,1,2,4...
sum_(n=1)^10 2^(n-2)
S_10=511.5
500
Given f(x)=x^3+4 , find the derivative and the equation of the tangent line at x=-1
Derivative: f'(x)=3x^2
Tangent Line: y=3x+6
500
Solve on the interval from [0,2pi]
1+cosx=sinx
x=pi/2, pi