| Derivatives | Integrals | Limits | Particle Motion | More Integrals |
|---|---|---|---|---|
|
e^x
(e^x)' =
|
ln lxl + C
∫1/x dx
|
limit as x approaches infinite from the right of f(x)=a
or limit as x approaches infinite from the left of f(x)=a
y=a is a horizontal asymptote if
|
((V(b)-V(a)) / (b-a))
or (1/(b-a)) integral from a to b a(t) dt
Average Acceleration
|
The anti-derivative
What is an indefinite integral?
|
|
-csc^2 (x)
(cot(x))' =
|
((a^x) / (lnx)) + C
∫a^x dx
|
Limit as x approaches a of C=C
limit as x approaches a of C=
|
v(t) and a(t) have the same signs
Speed is increasing if
|
inverse cot(x) + C
∫- (1/(1+x^2)) dx
|
|
sec(x)tan(x)
(sec(x))' =
|
(1/k) sin(kx+b) +C
∫cos(kx+b) dx
|
(limit as x approaches a of f(x))^P
limit as x approaches a of (f(x)^P)
|
v(t) and a(t) have opposite signs
Speed is decreasing if
|
inverse sec(x) + C
∫1/((lxl)(√(x^2)-1) dx
|
|
-csc(x)cot(x)
(csc(x))' =
|
(-1/k) cos(kx+b) +C
∫sin(kx+b) dx
|
C times limit as x approaches a of f(x)
limit as x approaches a (c times f(x))
|
integral from a to b v(t) dt
Net Distance=
Displacement= |
inverse csc(x) + C
∫-1/((lxl)(√(x^2)-1) dx
|
|
sec^2 (x)
(tan(x))' =
|
(-1/k) (e^(kx+b)) + C
∫e^(kx+b) dx
|
limit as x approaches a from the right of f(x)= infinite or negative infinite
or limit as x approaches a from the left of f(x)= infinite or negative infinite
x=a is a vertical asymptote if
|
integral from a to b lv(t)l dt
Total Distance=
|
inverse tan(x) + C
∫(1/(1+x^2)) dx
|
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