Series
∑ arn when absolute value of r < 1
Converges
Integration by parts
∫udv=uv-∫vdu
dy/dx=
What is (dy/dt)/(dx/dt)?
How many petals does this polar equation's graph have?
Let @=theta
r=3cos(3@)
What is 3?
Base equation for Taylor polynomial
Pn(x) = f(a) + f'(a)(x-a) + (f''(a)/2!)(x-a)^2 + (f'''(a)/3!)(x-a)^3 + ... + (f^(n)(a)/n!)(x-a)^n
Which series are only used to test for convergence?
Alternating Series Test & Telescoping Series Test
Partial Fraction Decomposition
∫((px+q)/(x-a)(x-b))dx = A/(x-a) + B/(x-b)
d2y/dx2
What is ((dy/dt)/(dx/dt))/(dx/dt)?
Formula for the area bounded by a polar graph.
What is 1/2∫(ba r2)dt?
ex
1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + ... + (x^n)/n!
∑(-1)n+1an is the standard format for which test?
Alternating Series Test
Arc Length
∫ab √1+(f'(x))2dx
Arc length formula for parametric equations.
L = ∫[a,b] √( (dx/dt)2 + (dy/dt)2 ) dt
What way does this polar graph open and along which axis?
Let @=theta
r-a=-bcos@
What is leftwards along the x axis?
cos(x)
1- x2/2! + x4/4! - x6/6! +...+ x2n/(2n)!
Which test takes the limit of two compared series in the form of an/bn and determines convergence of the original function given, an?
Limit Comparison Test
Improper Integrals
∫a∞ f(x)dx= lim (b->∞) ∫ab f(x)dx
Find the derivative of the parametric equation:
x=t5+t
y=2t-5
What is dy/dx=2/((5t4)+1)?
What way does this polar graph open and along which axis?
r=a+bcos@
Let @=theta
What is rightwards along x axis.
sin(x)
x - x^3/3! + x^5/5! - x^7/7! + ... = ∑ (-1)^n * x^(2n+1) / (2n+1)! for n = 0 to ∞
When p > 1 in ∑ 1/np does the series converge or diverge?
Converges
d/dx ∫axf(t)dt = f(x)
Second Fund. Thm. of Calc
Find the second derivative of the parametric equation:
x=4t3
y=10t
What is (10/12t2)/12t2?
What way does this polar graph open and along which axis?
Let @=theta
a+bsin@=r
What is upwards along the y axis?
1/(1+x)
1 + x + x2 + x3 + xn