What is the limit as y approaches 0 of (ysin(y))/(11y^2) ?

The limit as y approaches 0 of (ysin(y))/(11y^2) is 1/11

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limit as y approaches 0 of (ysin(y))/(11y^2)

y \to 0 lim (\frac{y sin ( y )}{11 y ^{2}})

\frac{1}{11}

Decimal Notation

0.09090 \dots

Solution steps

y \to 0 lim (\frac{y sin ( y )}{11 y ^{2}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{11} \cdot y \to 0 lim (\frac{y sin ( y )}{y ^{2}})

Cancel the common factor:

y

= \frac{1}{11} \cdot y \to 0 lim (\frac{sin ( y )}{y})

Apply L'Hopital's Rule

: y \to 0 lim (\frac{cos ( y )}{1})

= \frac{1}{11} \cdot y \to 0 lim (\frac{cos ( y )}{1})

Plug in the value

y = 0

= \frac{1}{11} \cdot \frac{cos ( 0 )}{1}

Simplify

\frac{1}{11} \cdot \frac{cos ( 0 )}{1} : \frac{1}{11}

= \frac{1}{11}

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x \to 0 lim (\frac{1}{x} - \frac{1}{2 x ^{2}})

What is the limit as y approaches 0 of (ysin(y))/(11y^2) ?
The limit as y approaches 0 of (ysin(y))/(11y^2) is 1/11