What is the limit as h approaches 0 of ((1+h)^6-1)/h ?

The limit as h approaches 0 of ((1+h)^6-1)/h is 6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as h approaches 0 of ((1+h)^6-1)/h

h \to 0 lim (\frac{( 1 + h ) ^{6} - 1}{h})

6

Solution steps

h \to 0 lim (\frac{( 1 + h ) ^{6} - 1}{h})

Simplify

\frac{( 1 + h ) ^{6} - 1}{h} : (h + 2) ((h + 1)^{4} + (h + 1)^{2} + 1)

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

Plug in the value

h = 0

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

Simplify

(0 + 2) ((0 + 1)^{4} + (0 + 1)^{2} + 1) : 6

= 6

\int (- 6 x^{2} + 4 x - 4 x cos (x)) d x

\int_{0}^{8} (8 - x) d x

\int (x^{2} 3^{3} + 5) d x

\int \frac{e ^{2 x}}{2 + e ^{x}} d x

\frac{1}{4} x^{2} - \frac{1}{2} ln (x)

What is the limit as h approaches 0 of ((1+h)^6-1)/h ?
The limit as h approaches 0 of ((1+h)^6-1)/h is 6