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sin(u)
cos(u)
cos(u)
-sin(u)
tan(u)
sec2(u)
cot(u)
-csc2(u)
sec(u)
sec(u)tan(u)
csc(u)
-csc(u)cot(u)
ln(u)
1/u
eu
eu
sin-1(u)
cos-1(u)
tan-1(u)
cot-1(u)
Limit from the left of f(x) as x → a
Limit from the right of f(x) as x → a
Definition of Continuity
f(a) is defined
Limit from left = limit from right
Overall limit = f(a)
Chain rule
f’(u) * u’
Product Rule
uv’ + u’v
Quotient Rule
Intermediate Value Theorem
If f is continuous on the closed interval [a,b], where f(a) ≠ f(b) and k is a number between f(a) and f(b), then there is atleast one number c in (a, b) such that f(c) = k.
Mean Value Theorem
If f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c such that:
L’Hopital’s Rule
Critical Points
If f(x) is defined at x = c, then f(x) has a critical point at x = c if f’(c) = 0 OR f’(c) is undefined.
Global Minimum
f(c) < all other values of f(x)
Global Maximum
f(c) > all other values of f(x)
Extreme Value Theorem
If f is continuous on the closed interval [a, b], then f has both an absolute minimum value and absolute maximum in the interval.
F + G
F - G
FG
Fn
F/G
1
0
Fundamental Theorem of Calculus
Corollary to FTC
If continuous on [a, b] and x=c on (a, b) then…
(MVT/average value for integrals)
Disk Method
Washer Method
General volume equation
Arc Length (rectangular)
velocity
s’(t)
acceleration
s’’(t) = v’(t)
Speed (parametric and rectangular)
Displacement
Average velocity
Euler’s Method
Integration By Parts
Logistics