All Formulas Except Chp 5 Flashcards
|x|
{x if x>=0 and -x if<0
e
lim n>∞(1+(1/n))^n
f’(x)- definition
f’(x)= limn-∞ (f(x*h)-f(x))/h
f’(a)- definition
lim x-a (f(x)-f(a))/(x-a)
Average rate of change of f(x) on [a,b]
( f(b)-f(a)) / (b-a)
Rolle’s Theorem
If f is continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b), then there is at least one number c on (a,b) such that f’(c)=0.
Mean Value Theorem
If f is continuous on [a,b] and differentiable on (a,b), then there exists a number c on (a,b) such that f’(c)=(f(b)-(f(a))/(b-a)
Intermediate Value Theorem
If f is continuous on [a,b] and k is any number between f(a) and f(b), then there is at least one number c between a and b such that f(c)=k.
sin2x
2sinxcosx
cos2x
cos^2x-sin^2x
1-2sin^2x
2cos^2x-1
cos^2x
(1+cos2x)/2
sin^2x
(1-cos^2x)/2
d/dx[c]
0
d/dx[uv]
uv’*vu’
d/dx[f(g(x))]
f’(g(x))*g’(x)
d/dx[sinu]
cosu(du/dx)
d/dx[tanu]
sec^2u (du/dx)
d/dx[secu]
secutanu(du/dx)
d/dx [lnu]
(1/u)*(du/dx)
d/dx[e^u]
e^u (du/dx)
d/dx [arcsinu]
1/(√1-u^2) *du/dx
d/dx [arctanu]
1/(1+u^2) * du/dx
d/dx [arcsecu]
1/(|u|√u^2-1) * du/dx
(F^-1)(a)
1/f’(f^-1(a))
∫cosu
sinu+ C
∫sec^2udu
tanu+C
∫secutanu du
secu+ C
∫ 1/u du
ln|u| + C
d/dx [x^n]
nx^n-1
d/dx [u/v]
(vu’-uv’)/v^2
d/dx [cosu]
-sinu+C
d/dx[cotu]
-csc^2u (du/dx)
d/dx [cscu]
-cscucotu (du/dx)
d/dx [logau]
1/ulna (du/dx)
d/dx[a^u]
a^ulna(du/dx)
∫sinu du
-cosu + C
∫csc^2u du
-cotu+C
∫cscucotu du
-cscu + C
∫tanu du
-ln|cosu| + C
∫secu du
ln|secu+tanu| +C
∫e^u du
e^u +C
∫du/(u√u^2-a^2)
1/a arcsec (|u|/a) +C
∫du/ (√a^2-u^2)
arcsin(u/a) +C
∫cotu du
ln|sinu| + C
∫cscu du
-ln|cscu+cotu| + C
∫a^u du
a^u/lna +C
∫du/(u^2+a^2)
(1/a) arctan(u/a) + C
