What is the limit as h approaches 0 of (7(a+h)^2-7a^2)/h ?

The limit as h approaches 0 of (7(a+h)^2-7a^2)/h is 14a

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limit as h approaches 0 of (7(a+h)^2-7a^2)/h

h \to 0 lim (\frac{7 ( a + h ) ^{2} - 7 a ^{2}}{h})

14 a

Solution steps

h \to 0 lim (\frac{7 ( a + h ) ^{2} - 7 a ^{2}}{h})

Simplify

\frac{7 ( a + h ) ^{2} - 7 a ^{2}}{h} : 7 (h + 2 a)

= h \to 0 lim (7 (h + 2 a))

Plug in the value

h = 0

= 7 (0 + 2 a)

Simplify

= 14 a

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What is the limit as h approaches 0 of (7(a+h)^2-7a^2)/h ?
The limit as h approaches 0 of (7(a+h)^2-7a^2)/h is 14a