limit as x approaches 0 of ((1+x)^5-1)/x

解答

x \to 0 lim (\frac{( 1 + x ) ^{5} - 1}{x})

5

求解步骤

x \to 0 lim (\frac{( 1 + x ) ^{5} - 1}{x})

化简

\frac{( 1 + x ) ^{5} - 1}{x} : x + (x + 1)^{4} + (x + 1)^{3} + (x + 1)^{2} + 2

= x \to 0 lim (x + (x + 1)^{4} + (x + 1)^{3} + (x + 1)^{2} + 2)

代入值

x = 0

= 0 + (0 + 1)^{4} + (0 + 1)^{3} + (0 + 1)^{2} + 2

化简

0 + (0 + 1)^{4} + (0 + 1)^{3} + (0 + 1)^{2} + 2 : 5

= 5

x \to 16 - lim (\frac{8}{11 + 2 ^{\frac{1}{x - 16}}})

\int - 2 x^{4} - 4 x^{2} - 5 d x

\frac{d}{d x} (cot (\frac{π}{2}))

d er i v a t i v e (f (6 x))^{2} + 3

\frac{d}{d y} (y^{\frac{3}{2}})