Section 1
Preview this deck
d/dx(sinx)
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 14, 2020
Cards (73)
Section 1
(50 cards)
d/dx(sinx)
cosx
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]
v(t)>0
p(t) is moving right
If f'(x)<0
f(x) is decreasing
d/dx(a^u)
a^u(lna)(u')
p'(t)
v(t)= velocity
If f'(x)>0
f(x) is increasing
∫sec²x dx
tanx+C
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]
a(t)<0
v(t) decreasing
If f''(x)<0
f(x) is concave down & f'(x) is decreasing
∫k dx [k IS A CONSTANT]
kx+C
limit as x approaches 0: 1-cosx/x
0
d/dx(cscx)
-cscxcotx
∫cscxcotx
-cscx+C
d/dx(secx)
secxtanx
p''(t) or v'(t)
a(t)= acceleration
∫(e^kx)dx
ekx/k +C
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) increasing
d/dx(cosx)
-sinx
∫secxtanx dx
secx+C
Extreme Value Theorem
if f(x) is continuous on [a,b], then f(x) has an absolute max or min on the interval
v(t)<0
p(t) is moving left
∫(1/x)dx
ln|x|+C
v(t) and a(t) has same signs
speed of particle increasing
d/dx(cotx)
-csc²x
∫sinx dx
-cosx+C
1st fundamental theorem of calculus
(bounded by a to b) ∫f(x)dx= F(b)-F(a)
p(t), x(t), s(t)
means position function
d/dx(e^u)
e^u(u')
If f''(x)>0
f(x) is concave up & f'(x) is increasing
Product rule of f(x)g(x)
f'(x)g(x)+g'(x)f(x)
∫cosx dx
sinx+C
Continuity Rule
If the limit exists (aka left limit and right limit are equal), and the limit equals the function at that point.
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
v(t)=0
p(t) is at rest or changing direction
Basic Derivative
f(x^n)= nX^(n-1)
a(t)=0
v(t) not changing
If f''(x)=0
f(x) has a point of inflection & f'(x) has a max or min
Chain rule of f(x)^n
nf(x)f'(x)
v(t) and a(t) has different signs
speed of particle decreasing
Alternate Definition of Derivative
limit (as x approaches a number c)= f(x)-f(c)/x-c x≠c
d/dx(lnu)
u'/u
∫csc²x dx
-cotx+C
∫(x^n)dx
x^(n+1)∕(n+1) +C
d/dx(tanx)
sec²x
limit as x approaches 0: sinx/x
1
Quotient rule of f(x)/g(x)
g(x)f'(x)-f(x)g'(x)/g(x)²
Section 2
(23 cards)