FlashMath | calculus

derivatives

d/dx (xⁿ) =

nxⁿ⁻¹

d/dx (eˣ) =

eˣ

d/dx (ln(x)) =

1/x

d/dx (sin(x)) =

cos(x)

d/dx (cos(x)) =

-sin(x)

d/dx (tan(x)) =

sec²(x)

integration

∫ xⁿ dx =

xⁿ⁺¹ / (n + 1) + C

∫ eˣ dx =

eˣ + C

∫ 1/x dx =

ln|x| + C

∫ sin(x) dx =

-cos(x) + C

∫ cos(x) dx =

sin(x) + C

∫ sec²(x) dx =

tan(x) + C

limits

lim x → 0 (sin(x)/x) =

1

lim x → 0 (1 - cos(x))/x² =

1/2

lim x → 0 (eˣ - 1)/x =

1

lim x → ∞ (1 + 1/x)ˣ =

e

lim x → 0+ ln(x) =

-∞

lim x → 0 (tan(x)/x) =

1

fundamental theorems

First Fundamental Theorem of Calculus =

F'(x) = f(x)

Rolle's Theorem =

f'(c) = 0

Second Fundamental Theorem of Calculus =

∫ [a, b] f(x) dx = F(b) - F(a)

Taylor Series =

f(x) = Σ (fⁿ(a)/n!) (x - a)ⁿ

Mean Value Theorem (MVT) =

f'(c) = [f(b) - f(a)]/(b - a)

L'Hôpital's Rule =

lim x→a f(x)/g(x) = f'(x)/g'(x)

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