math midterm (chapter 1 and 2, trig to know)

indeterminate forms

0/0, infinity/infinity, infinity - infinity

tan^2x + 1

sec^2x

1 + cot^2x

csc^2x

squeeze theorem (two officers and a drunk theorem)

if f(x) is always smaller than or equal to g(x) and always bigger than or equal to h(x), and the two functions converge at L when x=c, lim x->c = L

lim x->0 (sin x)/x

1

lim x->0 (1- cos x)/x

0

infinite discontinuity

vertical asymptote

removable discontinuity

a "hole" in a graph

jump discontinuity

there is a limit from + and from - but are unequal

college board conclusion continuity

lim x -> p- (blah) = a, lim x-> p+ (meow) = a, f(x) = a

since lim x->p- f(x) = lim x->p+ f(x) = f(x), we know that f(x) is continuous at x = a

intermediate value theorem

If f is continuous on [a,b] and k is a number between f(a) and f(b), then there is at least one number c such that f(c)=k

derivative formula with x

lim x->a ( f(x)-f(a) )/ (x-a)

derivative formula with h

lim h->0 ( f(a+h)-f(a) )/ h

nondifferentiability

corner, cusp, vertical tangent, discontinuity

power rule

nx^(n-1)

product rule

f(x) * g'(x) + f'(x) * g(x)

quotient rule

g(x)f'(x)-f(x)g'(x) /g(x)^2

derivative sin(x)

cos x

derivative cos(x)

-sin x

derivative tan(x)

sec^2 x

derivative cot(x)

-csc^2 x

derivative sec(x)

sec x * tan x

derivative csc(x)

- csc x * cot x