Exam One Info Flashcards
Log linear plot
for exponentials take log of y= C•B^x
Log log plot
Log x and y, for power functions., y = CX^2
Exponential decay/growth equation
N(t) = N(0) x R^t R= rate of doubling N(0) = initial pop t = time unit
Slope formula for exponentials
Log ys over Xs slope= under x
Slope formula for power functions
Log ys over log xs slope = exponent
Squeeze theroem
Find lim x with y<x<z so find the lim of both sides and find x
Intermediate value theroem
Must have continuous function. Solution exists if there are different signs with the values of x. 0 if they add to 0
DNE by oscillation examples
(-2)^x or cos(x)
Lim to inf of Cosx/x
0
Lim of (Cos(2x)-1) / 3x to 0
Rewrite into the identities and the multiply by inverse of the internals
Leading terms
Use with lims to inf and use the first term on top and bottom
Lim to inf for zero over zero
Do algebra
Lim to inf if nonzero over zero
Inf, -inf or DNE keep track of signs
Union
Only use union for holes not piecewise
Intervals of continuity
Pieces you draw without lifting pencil
Sequence form
An = Fn
Recursive formula
An =An-1 •r
Intermediate value theroem
Prove that for the countinous chunk, equation goes through 0 or given value
Bisection method
Use intermediate theorem, then find the midpoint. Figure out if 0 is still between them, and do intermediate theroem again. Repeat till zero or as necessary
