Level 549 Level 551
Level 550

Calculus AB Theorems II


52 words 0 ignored

Ready to learn       Ready to review

Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

All None

Ignore?
sin(-x)
-sinx (odd)
cos(-x)=
cos(x) (even)
0
f '(x)=
f'(x)=d(cu)/dx=
cu'=c du/dx
f'(x)=d(u^n )/dx=
nu^(n-1) (u')
f'(x)=d(uv)/dx=
uv'+vu'
f'(x)=d(u/v)/dx=
(vu'-uv')/v^2
f'(u)=d(1/u)/dx=(d(u^(-1)))/dx
-1u^(-2) du/dx
d f(g(x))/dx=
f^' (g(x)) g^' (x)
f'(x)=d(e^u )/dx=
e^u u'=e^u du/dx
f'(x)=d(a^u )/dx=
a^u lna u^'=a^u lna du/dx
f'(x)=d/dx(lnu)=
1/u u'=1/u du/dx
f' (x)=d/dx(loga (u)=
1/lna (1/u) u'=
d/dx (g(x))=
1/(f' (g(x)))
f'(x)=d/dx(sinu)=
cos(u)u'=cos(u) du/dx
f'(x)=d/dx(cotu)=
(-csc^2)(u) u'= -csc^2(u) du/dx
f'(x)=d/dx(cosu)=
-sin(u)u'=-sin(u) du/dx
f'(x)=d/dx(tanu)=
sec^2(u) u'=sec^2(u) du/dx
f'(x)=d/dx(arccscu)=
-1/(|u|√(u^2-1)) u'=-1/(|u|√(u^2-1)) du/dx
f'(x)=d/dx(secu)=
sec(u) tan(u) u'=sec(u)tan(u)du/dx
f'(x)=d/dx(cscu)=
-csc(u)cot(u) u'=-csc(u)cot(u)du/dx
f'(x)=d/dx(arcsecu)
1/(|u|√(u^2-1)) u^'=1/(|u|√(u^2-1)) du/dx
f'(x)=d/dx(arctanu)=
1/(u^2+1) u'
f'(x)=d/dx(arccotu)=
-1/(u^2+1) u'=-1/(u^2+1) du/dx
f'(x)=d/dx(arcsinu)=
1/√(1-u^2 ) u'=1/√(1-u^2 ) du/dx
f'(x)=d/dx(arccosu)
-1/√(1-u^2 ) u'=-1/√(1-u^2 ) du/dx
If f(x) is continuous on [a,b], the Extreme Value Theorem states:
f(x) must have an absolute maximum and an absolute minimum on [a,b].
f' (c)=(f(b)-f(a))/(b-a)
If f(x) is continuous on [a,b] and differentiable on (a,b), the Mean Value Theorem guarantees that there is a number c between a and b such that ________
f' (c)=0
If f(x) is continuous on [a,b] and differentiable on (a,b), Rolle's Theorem guarantees that if f(a)=f(b), there is a number c between a and b such that ________
increasing
If f^' (x)>0 on an interval, then f is ______________________ on the interval.
decreasing
If f^' (x)<0 on an interval, then f is ______________________ on the interval.
Same; opposite
If a particle is speeding up, its velocity and acceleration have the_____________________________sign. If a particle is slowing down, its velocity and acceleration have ___________________________________signs.
Local Max of f(x)
(c, f(c)) is a ______________________________________________________________________________
Local Min of f(x)
(c, f(c)) is a ______________________________________________________________________________
e^u + c
∫ e^u du
∫u^n du =
(u^(n+1))/(n+1) +C , n≠ -1
ln |u|+C
∫1/u du =
-cosu+C
∫sinu du
sinu+C
∫cosu du
tanu+C
∫sec^2 u du
-cotu+C
∫csc^2u du
secu+C
∫tanu secu du
-cscu+C
∫cotu cscu du
a^u/lna +C
∫a^u du =
[a,b]
1/(b-a) ∫a^bf(x)dx
∫a^b|v(t)|dt
Given velocity v(t), the total distance travelled over time a,b is
1/(b-a) ∫a^b v(t)dt
Given velocity v(t), the average velocity of an object over time a,b is
F(b)-F(a)
Derivative of f(x), then ∫a^b f(x)dx is
A= 1/2 (b_1+b_2 )h
The formula for the area of a trapezoid w/ bases b1, b2 and height h
A=π(R^2-r^2)
The formula for the area of a washer with large radius R and small radius r
(√3/4) s^2
The equation for the area of an equilateral triangle with side length s.
1/4 h^2
The formula for the area of a right iscosceles triangle with known hypotenuse