Show:
Derivatives
Integrals
Limits
Series
Name the Rule/Method
100
Find the derivative of: 2x^3
What is 6x^2
100
Evaluate ∫(cosx)dx
What is sinx+c
100
Find the limit: lim┬(x→-3)lx+3l
What is 0
100
The first four terms of the series: 1/(1-x)
What is 1+x+(x^2)+(x^3)+...
100
If f is cont. on [a/b] amd differentiable on (a,b), then there exists c on a
What is Mean Value Theorem
200
The derivative of cos^-1x
What is -1/√(1-x^2)
200
Find ∫x^ndx in terms of n
What is (x^(n+1)/n+1)+c
200
Find the limit: lim┬(x→-1)x^2+3x+2/x+1
What is 1
200
The first four terms of the series: cosx
What is 1-(x^2/2!)+(x^4/4!)-(x^6/6!)+...
200
Definition: The limit, L, of a function, f(x), as x approaches a exists iff lim┬(x→a-)f(x)=lim┬(x→a+)f(x) = L
What is a Limit
300
Calculate the derivate of: y=3sinx/cosx
What is y'=3sec^2x
300
Evaluate ∫cosxcos(sinx)dx
What is sin(sinx)+c
300
Find the limit: lim┬(x→∞) (3x^7-5x^3+2)/(6x^7+12x^4-81)
What is 1/2
300
The first four terms of the series: cos(x^2)
What is 1-((x^2)^2/2!)+((x^2)^4/4!))-((x^2)^6/6!)+...
300
*Involves vertical asymptote or +/- ∞ *A change is required to eliminate them *Use limits
What is Improper Integrals
400
Calculate f' in terms of g' for f(x)=x^2g(x)
What is x^2g'(x)+2xg(x)
400
Evaluate ∫cosxe^(sinx)dx
What is e^(sinx)+c
400
lim┬(x→0)tan(πx)/ln(1+x)
What is π
400
The first four terms of the series: 1/(1+x^3)
What is 1-x^3+x^6-x^9+...
400
Estimates a function value when the differential equation cannot be solved
What is Euler's Method
500
Calculate y' for x^2+siny=xy
What is y-2x/cosy-x
500
Evaluate ∫xsin(3x^2)dx
What is (-cos(3x^2)/6)+c
500
lim┬(h→0) (sin^2(x+h)-sin^2x)/h
What is 2sinxcosx
500
The first four terms of the series: 2sin(-x)
What is 2((-x)-((-x)^3/3!)+((-x)^5/5!)-((-x)^7/7!)+...)
500
*Equations look like r=...Ѳ (usually symmetric) *Find beginning/ending or intersection points (Angles) *Formula to be memorized A=∫θ1^θ2 r^2/2 dθ
What is Area of Polar Curve