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

The limit as x approaches 5/2 of (4x^2-25)/(2x-5) is 10

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

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

10

Solution steps

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

Simplify

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

= x \to \frac{5}{2} lim (2 x + 5)

Plug in the value

x = \frac{5}{2}

= 2 \cdot \frac{5}{2} + 5

Simplify

2 \cdot \frac{5}{2} + 5 : 10

= 10

x \to - \infty lim (x^{2} + x)

x \to - 3 lim (x^{2} + 2 x - 5)

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

x \to 0 lim ((sec (x))^{4 x})

x \to 0 + lim (- \frac{sin ( x )}{2 \cdot x})

What is the limit as x approaches 5/2 of (4x^2-25)/(2x-5) ?
The limit as x approaches 5/2 of (4x^2-25)/(2x-5) is 10