Terms  Definitions 

Integral 
Accumulation

(d/dx)(tan(x)) 
(sec(x))^2

Quotient Rule 
(uv'vu')/v²

slope of horizontal line 
zero

Product Rule 
uv' + vu'

absolute value of velocity 
speed

slope of vertical line 
undefined

Convergent 
If lim(a(n) > infinity) exists

Integral of: (sec(x))^2 dx 
tan(x) + c

Trapezoidal Rule 
Area of Trapezoid= ΔX/2 (f(Xk)+f(Xk+1))
Tn=ΔX/2(f(Xo)+2f(X1)+2f(X2)+...+2f(Xn1)+f(Xn)) 
When f '(x) is negative, f(x) is 
decreasing

y = ln(x), y' = 
y' = 1/x

y = sec(x), y' = 
y' = sec(x)tan(x)

mean value theorem 
if f(x) is continuous and differentiable, slope of tangent line equals slope of secant line at least once in the interval (a, b)
f '(c) = [f(b)  f(a)]/(b  a) 
left riemann sum 
use rectangles with leftendpoints to evaluate integral (estimate area)

Particle is moving to the left/down 
velocity is negative

y = a^x, y' = 
y' = a^x ln(a)

derivative of parametrically defined curve x(t) and y(t) 
dy/dx = dy/dt / dx/dt

When f '(x) changes fro positive to negative, f(x) has a 
relative maximum

y = cot⁻¹(x), y' = 
y' = 1/(1 + x²)

First Derivative (Parametrics) 
dy/dx = (dy/dt)/(dx/dt) where dx/dt != 0

definite integral 
has limits a & b, find antiderivative, F(b)  F(a)

y = sin⁻¹(x), y' = 
y' = 1/√(1  x²)

geometric series test 
general term = a₁r^n, converges if 1 < r < 1

Derivatives of Trig functions 
(sinx)' = cosx
(cosx)' = sinx (tanx)' = sec^2x (cotx)' = csc^2x (secx)' = secxtanx (cscx)' = cscxcotx 
When is a function not differentiable 
corner, cusp, vertical tangent, discontinuity

To find absolute maximum on closed interval [a, b], you must consider... 
critical points and endpoints

y = ln(x)/x², state rule used to find derivative 
quotient rule

Alternate definition of derivative 
limit as x approaches a of [f(x)f(a)]/(xa)

y = x cos(x), state rule used to find derivative 
product rule

Theorem: If lim of a(n) = 0... 
lim of a(n) = 0

y = log (base a) x, y' = 
y' = 1/(x lna)

Extreme Value Theorem 
If f is a continuous function on a closed interval [a,b], then f has both a maximum and minimum value on the interval

second derivative of parametrically defined curve 
find first derivative, dy/dx = dy/dt / dx/dt, then find derivative of first derivative, then divide by dx/dt

If f '(x) = 0 and f"(x) > 0, 
f(x) has a relative minimum

A function is continuous if... 
1. f(a) exists
2. lim as x> a of f(x) exists 3. lim as x>a of f(x)=f(a) 
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