final Flashcards
∫a^x dx
((a^x)/ln(a)) + c
∫e^ax dx
((e^ax)/a) + c
∫sec(x)tan(x) dx
sec(x) + c
∫csc(x)cot(x) dx
-csc(x) + c
∫sec^2 (x) dx
tan(x) + c
∫csc^2(x) dx
-cot(x) + c
∫(1/(1+x^2)) dx
arctan(x) + c
∫(1/(√1-x^2)) dx
arcsin (x) + c
∫tan(x) dx
-ln|cos(x)| + c
F(x) + C
= ∫f(x) dx
d/dx (position)
= velocity (v(t))
d/dx (velocity)
= acceleration (a(t))
Riemann summation right
i=1, n
Riemann summation left
i=0, n-1
ix
a+ delta(x)i
FTC P1
F’(x) = f(x)
FTC P2: area under curve from a to b
∫ f(x)dx = F(b) - F(a)
indefinite integral
no given interval, will have function as answer (x’s in answer)
definite integral
given interval, [a,b], and number as answer (no x’s)
0/0 or ∞/∞
L’hopital rule
definition of derivative, lim to 0
(f(x+h) - f(x))/h)
definition of derivative, lim to a
(f(x) - f(a))/(x-a)), a is derivative of f(x)
linearization
L(x) = f(a) - f’(a)(x-a)
mean value theorem
continuous in (a,b)
differentiable on [a,b]
there exists a c in (a,b) such that f’(c) = (f(b) - f(a)) / (b-a))
squeeze theorem
extreme value theorem
intermediate value theorem
rolle’s theorem
continuous on [a,b]
differentiable on (a,b)
f(a) = f(b)
then there exists a c in (a,b) such that f’(c) = 0
