Find the limit of lim x - 23 x2-x-10-x2-4

At x=2, the value of the given rational function takes the form 0/0 ∴lim_x→ 23x^2 x 10/x^2 4=lim_x→ 2(x 2)(3x+5)/(x 2)(x+2) =lim_x→ 23x+5/x+2 =3(2)+5/2+2 =11 ...

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Byju's Answer

Standard XII

Mathematics

Local Minima

Find the limi...

Question

Find the limit of ${lim}_{x \to 2} \frac{3 x^{2} - x - 10}{x^{2} - 4}$

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Solution

At x=2, the value of the given rational function takes the form $\frac{0}{0}$
$∴ {lim}_{x \to 2} \frac{3 x^{2} - x - 10}{x^{2} - 4} = {lim}_{x \to 2} \frac{(x - 2) (3 x + 5)}{(x - 2) (x + 2)} = {lim}_{x \to 2} \frac{3 x + 5}{x + 2} = \frac{3 (2) + 5}{2 + 2} = \frac{11}{4}$

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Find the limit of limx→23x2−x−10x2−4

At x=2, the value of the given rational function takes the form 00 ∴limx→23x2−x−10x2−4=limx→2(x−2)(3x+5)(x−2)(x+2)=limx→23x+5x+2=3(2)+52+2=114

Find the limit of ${lim}_{x \to 2} \frac{3 x^{2} - x - 10}{x^{2} - 4}$

At x=2, the value of the given rational function takes the form $\frac{0}{0}$
$∴ {lim}_{x \to 2} \frac{3 x^{2} - x - 10}{x^{2} - 4} = {lim}_{x \to 2} \frac{(x - 2) (3 x + 5)}{(x - 2) (x + 2)} = {lim}_{x \to 2} \frac{3 x + 5}{x + 2} = \frac{3 (2) + 5}{2 + 2} = \frac{11}{4}$