What is the limit as h approaches 0 of (sin(2h))/(5h^2+7h) ?

The limit as h approaches 0 of (sin(2h))/(5h^2+7h) is 2/7

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limit as h approaches 0 of (sin(2h))/(5h^2+7h)

h \to 0 lim (\frac{sin ( 2 h )}{5 h ^{2} + 7 h})

\frac{2}{7}

Decimal

0.28571 \dots

Solution steps

h \to 0 lim (\frac{sin ( 2 h )}{5 h ^{2} + 7 h})

Apply L'Hopital's Rule

= h \to 0 lim (\frac{cos ( 2 h ) \cdot 2}{10 h + 7})

Plug in the value

h = 0

= \frac{cos ( 2 \cdot 0 ) \cdot 2}{10 \cdot 0 + 7}

Simplify

\frac{cos ( 2 \cdot 0 ) \cdot 2}{10 \cdot 0 + 7} : \frac{2}{7}

= \frac{2}{7}

What is the limit as h approaches 0 of (sin(2h))/(5h^2+7h) ?
The limit as h approaches 0 of (sin(2h))/(5h^2+7h) is 2/7