What is the limit as h approaches 0 of ((1+h)^7-1)/h ?

The limit as h approaches 0 of ((1+h)^7-1)/h is 7

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limit as h approaches 0 of ((1+h)^7-1)/h

h \to 0 lim (\frac{( 1 + h ) ^{7} - 1}{h})

7

Solution steps

h \to 0 lim (\frac{( 1 + h ) ^{7} - 1}{h})

Simplify

\frac{( 1 + h ) ^{7} - 1}{h} : h + (h + 1)^{6} + (h + 1)^{5} + (h + 1)^{4} + (h + 1)^{3} + (h + 1)^{2} + 2

= h \to 0 lim (h + (h + 1)^{6} + (h + 1)^{5} + (h + 1)^{4} + (h + 1)^{3} + (h + 1)^{2} + 2)

Plug in the value

h = 0

= 0 + (0 + 1)^{6} + (0 + 1)^{5} + (0 + 1)^{4} + (0 + 1)^{3} + (0 + 1)^{2} + 2

Simplify

0 + (0 + 1)^{6} + (0 + 1)^{5} + (0 + 1)^{4} + (0 + 1)^{3} + (0 + 1)^{2} + 2 : 7

= 7

What is the limit as h approaches 0 of ((1+h)^7-1)/h ?
The limit as h approaches 0 of ((1+h)^7-1)/h is 7