Calc 115 final yay

use def of derive to find derive and it doesn’t simplify…

find common denominator in the numerator or use conjugate roots

if f is fun and lim as x→ inf f(x)=L y=L is

a horizontal asymptote

if f is fun and lim as x→c f(x)= inf x=c is

a vertical asymptote

continuous def

lim h→a f(x)=f(a)

c is crit num of f if

f!(c ) = DNE, or 0

local means it is at the point of the triangle of chart

local max min meaning

what points check for looking for global max

crit points and end points

d/dt of a constant =

0

quotient rule

f!g-g!f/g²

cos²x + sin²x

= 1

d/dx sin(x+y) =

cos(x+y)*(1+dy/dx)

S sinx=

-cos x + c

S 1/x

ln |x| + c

if the func goes neg accum

is from func up to x axis and neg

e^-1

NOOOOOOO

horizontal asymptote

n<d - 0, n>d none, n=d the ratio (the coefficients)

find location of global min or max on closed interval

plug end points and crit points into og func

restrict tan interval to what for arc tan?

-pi/2, pi/2 one squiggly in between

e^4ln3

81

ln 4e³

ln 4 + 3

if a graph is inc from a to b, which has a larger value

b

S x^n dx =

x^(n+1)/n+1

exponent rules

multiply - add exponents, divide - subtract exponents

f(x) inc when

f!(x) >0

inflection points of f(x)

when f!(x) tan is flat (min or max)

when is f(x) cup

when f!!(x)>0 so when f!(x) slope is increasing/positive

if you can factor out the denominator

the asymptote does not exist

(f o g)! (x) =

f!(g(x) • g!(x)