What is the limit as x approaches-5/2 of ((8x^3+125))/(6x^2+23x+20) ?

The limit as x approaches-5/2 of ((8x^3+125))/(6x^2+23x+20) is -150/7

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limit as x approaches-5/2 of ((8x^3+125))/(6x^2+23x+20)

x \to - \frac{5}{2} lim (\frac{( 8 x ^{3} + 125 )}{6 x ^{2} + 23 x + 20})

- \frac{150}{7}

Decimal

- 21.42857 \dots

Solution steps

x \to - \frac{5}{2} lim (\frac{8 x ^{3} + 125}{6 x ^{2} + 23 x + 20})

Simplify

\frac{8 x ^{3} + 125}{6 x ^{2} + 23 x + 20} : \frac{4 x ^{2} - 10 x + 25}{3 x + 4}

= x \to - \frac{5}{2} lim (\frac{4 x ^{2} - 10 x + 25}{3 x + 4})

Plug in the value

x = - \frac{5}{2}

= \frac{4 ( - \frac{5}{2} ) ^{2} - 10 ( - \frac{5}{2} ) + 25}{3 ( - \frac{5}{2} ) + 4}

Simplify

\frac{4 ( - \frac{5}{2} ) ^{2} - 10 ( - \frac{5}{2} ) + 25}{3 ( - \frac{5}{2} ) + 4} : - \frac{150}{7}

= - \frac{150}{7}

x \to \infty lim (14 x)

x \to 1 lim (\frac{x + 1}{x})

x \to \infty lim (5 - (- 2))

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

t \to 0 lim (sin (\frac{1}{t}))

What is the limit as x approaches-5/2 of ((8x^3+125))/(6x^2+23x+20) ?
The limit as x approaches-5/2 of ((8x^3+125))/(6x^2+23x+20) is -150/7