limits
as x approaches infinity, the graph of a function approaches, but never crosses a predetermined y value.
What is a horizontal asymptote?
1d2+2d1
What is the product rule?
increasing the power by one, and dividing the coefficient by the power.
What is simple integration?
method for approximating the total area beneath a curve.
What is Riemann Sums?
cos(u)(u')
what is the derivative of sin(u)?
holes, jumps, and vertical asymptotes.
What is discontinuity?
(lowdhi-hidlow)/(low)2
What is the quotient rule?
f(0)+ ∫a->b[f'(x)]dx
What is start+accumulation?
x 2 4 6 8
y 3 7 18 2
=∫2(7+18+2)dx
What is a right riemann sum?
the written expression for the inverse of a trig function
arc
1. direct substitution
2. (0/0) simplify algebraically -> direct substitution
3. (#/0) sign analysis (3 limits)
What is limits algebraically?
decrease the power of a group by one and multiply the power in front, then tack on the derivative of the group.
What is the simple chain rule?
∫u'/u
ln|u|+c
x 2 4 6 8
y 3 7 18 2
=∫2(5+13.5+10)dx
What is midpoint riemann sum?
-sin(u)(u')
what is the derivative of cos(u)?
limit as h->0
[f(x+h)-f(x)]/h
What is the limit definition of derivative?
pointy points, vertical asymptotes, jumps.
What is non-differentiable?
d/dx ∫ from u->v f(x)dx
=f(v)v'-f(u)u'
What is the second fundamental theorem of calculus?
method for approximating the total area beneath a curve using trapezoids.
What is trapezoidal rule?
sec2(u)(u')
limit as x->2 (8-3x+12x2)
What is 50?
y= 2x3-4x2+8x+21
y'= ...
What is 6x2-8x+8?
∫[6x2+4x]dx
What is 2x3+2x2+c?
x 3 6 7 10
y 1 7 18 2
the area beneath the curve using a midpoint riemann sum is ...
∫[3(4)+1(12.5)+3(10)]dx
what is the derivative of arctan(x)?