Section 1
Preview this deck
∫(x^n)dx
Front
| 5 | 0 | ||
| 4 | 0 | ||
| 3 | 0 | ||
| 2 | 0 | ||
| 1 | 0 |
Active users
0
All-time users
0
Favorites
0
Last updated
6 years ago
Date created
Mar 1, 2020
Cards (73)
Section 1
(50 cards)
∫(x^n)dx
x^(n+1)∕(n+1) +C
v(t)=0
p(t) is at rest or changing direction
limit as x approaches 0: 1-cosx/x
0
d/dx(cosx)
-sinx
v(t) and a(t) has same signs
speed of particle increasing
Limit Definition of Derivative
limit (as h approaches 0)= F(x+h)-F(x)/h
If f'(x)=0
there is a max or min on f(x) [number line test]
p'(t)
v(t)= velocity
∫sinx dx
-cosx+C
d/dx(cotx)
-csc²x
If f''(x)<0
f(x) is concave down & f'(x) is decreasing
If f'(x)<0
f(x) is decreasing
d/dx(sinx)
cosx
∫(e^kx)dx
ekx/k +C
∫k dx [k IS A CONSTANT]
kx+C
d/dx(lnu)
u'/u
v(t)>0
p(t) is moving right
v(t)<0
p(t) is moving left
d/dx(e^u)
e^u(u')
Mean Value Theorem
if f(x) is continuous on [a,b] and differentiable on (a,b), there is at least one point (x=c) where f'(c)= F(b)-F(a)/b-a
∫secxtanx dx
secx+C
a(t)<0
v(t) decreasing
∫(1/x)dx
ln|x|+C
v(t) and a(t) has different signs
speed of particle decreasing
Continuity Rule
If the limit exists (aka left limit and right limit are equal), and the limit equals the function at that point.
p''(t) or v'(t)
a(t)= acceleration
Rolle's Theorem
if f(x) is continuous on [a,b] and differentiable on (a,b), and if f(a)=f(b), then there is at least one point (x=c) on (a,b) [DON'T INCLUDE END POINTS] where f'(c)=0
a(t)=0
v(t) not changing
1st fundamental theorem of calculus
(bounded by a to b) ∫f(x)dx= F(b)-F(a)
a(t)>0
v(t) increasing
∫sec²x dx
tanx+C
Intermediate Value Theorem
if f(x) is continuous on [a,b], then there will be a point x=c that lies in between [a,b]
d/dx(secx)
secxtanx
If f''(x)=0
f(x) has a point of inflection & f'(x) has a max or min
If f''(x)>0
f(x) is concave up & f'(x) is increasing
d/dx(cscx)
-cscxcotx
d/dx(a^u)
a^u(lna)(u')
∫cosx dx
sinx+C
d/dx(tanx)
sec²x
Extreme Value Theorem
if f(x) is continuous on [a,b], then f(x) has an absolute max or min on the interval
Quotient rule of f(x)/g(x)
g(x)f'(x)-f(x)g'(x)/g(x)²
Basic Derivative
f(x^n)= nX^(n-1)
Chain rule of f(x)^n
nf(x)f'(x)
p(t), x(t), s(t)
means position function
Alternate Definition of Derivative
limit (as x approaches a number c)= f(x)-f(c)/x-c x≠c
Product rule of f(x)g(x)
f'(x)g(x)+g'(x)f(x)
limit as x approaches 0: sinx/x
1
∫cscxcotx
-cscx+C
∫csc²x dx
-cotx+C
If f'(x)>0
f(x) is increasing
Section 2
(23 cards)