What is the limit as y approaches 5 of (25-y^2)/(y^2-4y-5) ?

The limit as y approaches 5 of (25-y^2)/(y^2-4y-5) is -5/3

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limit as y approaches 5 of (25-y^2)/(y^2-4y-5)

y \to 5 lim (\frac{25 - y ^{2}}{y ^{2} - 4 y - 5})

- \frac{5}{3}

Decimal Notation

- 1.66666 \dots

Solution steps

y \to 5 lim (\frac{25 - y ^{2}}{y ^{2} - 4 y - 5})

Simplify

\frac{25 - y ^{2}}{y ^{2} - 4 y - 5} : - \frac{y + 5}{y + 1}

= y \to 5 lim (- \frac{y + 5}{y + 1})

Plug in the value

y = 5

= - \frac{5 + 5}{5 + 1}

Simplify

- \frac{5 + 5}{5 + 1} : - \frac{5}{3}

= - \frac{5}{3}

\int \frac{sin ( 2 t + 1 )}{cos ^{2} ( 2 t + 1 )} d t

y^{^{'}} = \frac{1 - x}{y}

\frac{d}{d x} (- 3 tan (3 x))

\frac{d}{d x} (- a sin (x))

{\frac{( s + 2 ) ^{2}}{s ^{3}}}

What is the limit as y approaches 5 of (25-y^2)/(y^2-4y-5) ?
The limit as y approaches 5 of (25-y^2)/(y^2-4y-5) is -5/3