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Level 595

Calculus BC


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Absolute Convergence
∑An is convergent as well as ∑|An|
Integral Test
take integral and evaluate, if it goes to a number it is convergent, if there is ∞in it, its divergent
Comparison Test
after comparing remember to take the limit as n→∞ of an/bn and for convergence it must lie on the interval 0<L<∞
P series test
The p series is given by ∑1/(n^p), where p>0 by definition.
∑cⁿxⁿ=c₀+c₁x+c₂x²+c₃x³+...
Power series
∑xⁿ/n!
Series of e^x
∑(-1)ⁿ*(x²ⁿ⁺¹/(2n+1)!)
Series of sinx
∑(-1)ⁿ*(x²ⁿ/(2n)!)
Series of cosx
fⁿ⁺¹(z)(x+c)ⁿ⁺¹/(n+1)!
Lagrange error formula
cos²x
1 - sin²x
sec²x
1 + tan²x
cot²x
csc² - 1
sin(2x)
2sinx^2cosx
(1) cos(2x)
cos²x - sin²x
(2) cos(2x)
1 - 2sinx
(3) cos(2x)
2cos²x - 1
sin(A+B)
sinAcosB + sinBcosA
cos(a+b)
cosAcosB - sinAsinB
nxⁿ⁻¹
ƒ'(x) of xⁿ
(dy/dx) y = f(x) * g(x)
f(x) * g'(x) + g(x) * f'(x)
(dy/dx) y =f(x)/g(x)
g(x) * f'(x) - f(x) * g'(x) / g(x)²
f'(g(x)) * g'(x)
(dy/dx) y = f(g(x))
cosx
(dy/dx) y = sinx
-sinx
(dy/dx) y = cosx
sec²x
(dy/dx) y = tanx
-cscxcotx
d/dx (csc x) =
secxtanx
(dy/dx) y = secx
-csc²x
f'(x) of cot x
eⁿ
(dy/dx) y = eⁿ
aⁿlna
(a is a constant)
1/x
(dy/dx) y = lnx
1/xln(a)
(dy/dx) y = log_a(x)
1/√1-x²
(dy/dx) y = sin⁻¹x
-1/√1-x²
(dy/dx) y = cos⁻¹x
1/1+x²
(dy/dx) y = tan⁻¹x
-1/x√x²-1
(dy/dx) y = csc⁻¹x
1/x√x²-1
(dy/dx) y = sec⁻¹x
1/f'(f⁻¹(x))
(dy/dx) y = f⁻¹(x)
∫adx
ax+C
∫xⁿdx
(xⁿ⁺¹)/(n+1)+C
∫eⁿdn
eⁿ (+C)
∫aⁿdn
aⁿ/lna (+C)
∫(1/x)dx
ln|x|+C
∫sinx
-cosx (+C)
∫cosx
sinx (+C)
∫tanx
ln|secx| (+C)
∫cotx
ln|sinx| (+C)
∫sec²x
tanx (+C)
∫tan²x
tanx - x (+C)
∫secxtanx
secx (+C)
∫secx
ln|secx + tanx| (+C)
∫1/a² + x²
(1/a) (tan⁻¹) (x/a) (+C)
∫1/√a²-x²
sin⁻¹(x/a) (+C)