Section 1
Preview this deck
d/dx a^x
Front
| 5 | 0 | ||
| 4 | 0 | ||
| 3 | 0 | ||
| 2 | 0 | ||
| 1 | 0 |
Active users
0
All-time users
0
Favorites
0
Last updated
5 years ago
Date created
Mar 1, 2020
Cards (59)
Section 1
(50 cards)
d/dx a^x
(ln a) • a^x
d/dx ln x
1/x
d/dx loga x
1/((ln a)x)
Lim[x→0] (sin x)/x
1
Acceleration Function
a(t) = v'(t)
Average Value
⌠b │ f(x) dx • 1/(b - a) ⌡a
Lim[x→∞] (1 + (1/x))^x
e
Disk Method
d/dx arccsc x
-1/(│x│√(x^2 - 1) )
d/dx csc x
-csc x cot x
Power Rule
d/dx (x^n) = nx^(n-1)
Chain Rule
d/dx (f(g(x))) = f'(g(x)) • g'(x)
⌠ │ cos x dx ⌡
sin x + C
d/dx sec x
sec x tan x
d/dx arccos x
-1/√(1 - x^2)
d/dx cot x
-csc^2 x
Washer Method
d/dx sin x
cos x
Fundamental Theorem 2
⌠x d/dx │ f(t) dt = f(x) ⌡a
Velocity Function
v(t) = s'(t)
Lim[x→∞] c/(x^n)
0
⌠ │ sec x dx ⌡
ln │sec x + tan x│ + C
Mean Value Theorem
f'(c) = (f(b) - f(a))/(b - a)
⌠ │ du/u√(u^2 - a^2) ⌡
(1/a) arcsec (│u│/a) + C
d/dx arccot x
-1/(1 + x^2)
Quotient Rule
d/dx (f(x)/g(x)) = (g(x) f'(x) - f(x) g'(x))/(g(x))^2
Position Function
s(t)
Projectile Position Equation
s(t) = -1/2 g t^2 + Vo t + Ho; g = 9.8 m/s^2 = 32 ft/s^2
d/dx arctan x
1/(1 + x^2)
Trapezoidal Rule
((b -a)/2n) (f(a) + 2f(x1) + 2f(x2) + ... + 2f(x[n-1]) + f(b))
d/dx cos x
-sin x
Integration by Parts
⌠ ⌠ │u dv = uv - │ v du ⌡ ⌡
d/dx e^x
e^x
d/dx tan x
sec^2 x
Polar Area
⌠b 1/2 │ (r(Θ))^2 dΘ ⌡a
⌠ │ csc x dx ⌡
-ln │csc x + cot x│ + C
⌠ │ du/√(a^2 - u^2) ⌡
arcsin (u/a) + C
(f^-1)'(x)
1/(f'(f^-1(x)))
⌠ │ du/(a^2 + u^2) ⌡
(1/a) arctan (u/a) + C
Lim[x→0] (cos x - 1)/x
0
Exponential Growth/Decay
dy/dt = ky; y = Ne^kt
d/dx arcsin x
1/√(1 - x^2)
Arc Length
⌠ │ tan x dx ⌡
-ln │cos x│ + C
Fundamental Theorem 1
⌠b │ f(x) dx = F(b) - F(a); if F is the antiderivative of f ⌡a
Power Rule for Integrals
⌠ │ x^n dx = (x^(n + 1))/(n + 1) + C ⌡
⌠ │sin x dx ⌡
-cos x + C
⌠ │ cot x dx ⌡
ln │sin x│ + C
Product Rule
d/dx (f(x) • g(x)) = f(x) g'(x) + g(x) f'(x)
d/dx arcsec x
1/(│x│√(x^2 - 1) )
Section 2
(9 cards)