Derivatives
d/dx cos(x)
-sin(x)
Integral of sin(x)
-cos(x) + c
How do you find area of 2 equations
Top-bottom or right-left
How do you get velocity from f(x)
f’(x)
1+x+1/2!x2+1/3!x3+1/4!x4+…+ xn/n!
ex
d/dx (ln(x))
1/x
Integral of sec2(x)
tan(x)+c
How do you find length of curve
Integral of Square root(1+f’(x))
How do you get acceleration
f’’(x)
x-1/3!x3+1/5!x5-1/7!x7+…+ (-1)nx2n+1/(2n+1)!
Sin(x)
d/dx (xn)
nxn-1
Integral of xn
(xn+1)/n+1
Cross section of a Isosceles Triangle
Integral of 1/2 (top-bottom) dx
Position at time t
X(a)+ingigral x’(t) dt
Taylor Series
f(c)+f’(c)(x-c)+f’’(c)(x-c)2/2!+f’’’(c)(x-c)3/3!
d/dx [f(x)g(x)]
f(x)g’(x)+f’(x)g(x)
∫4𝑥6−2𝑥3+7𝑥−4𝑑𝑥
4/7x7-1/2x4+7/2x2-4x+c
Volume of a washer
Pi integral (R2)-(r2)dx
Speed
square root x’(t)+y’(t)
when does 1/pn converges
converges when p greater than 1
d/dx [f(x)/g(x)]
[g(x)f’(x)-g’(x)f(x)]/g(x)^2
∫(5x3)(15x4)
(5x3)3x5+(5/4x4)(15x4)
Volume of shell
2pi integral (r)(h)dx
Total distance
intigral of square root x’(t)+y’(t)
Does converge or diverge ∑(2n!)/5n+1
Diverges