Lim x- 2-x2-3x2-4-2-34-4-50-But the answer is -Where I am wrong- Please clarity the concept-

lim _x→ 2^ x^2 3x^2 4 lim _x→ 2 nx^2 3x^2 4 lim _n→ 0(2 n)^2 3(2 n)^2 4=2^3 32^2 4=10=∞ ...

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Theorems for Continuity

lim x→ 2-x2-3...

Question

$lim x \to 2^{-} \frac{x^{2} - 3}{x^{2} - 4} = \frac{- 2 - 3}{4 - 4} = \frac{- 5}{0} = - \infty$
But the answer is $+ \infty$
Where I am wrong. Please clarity the concept.

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This is a silly question but due to tension I am not able to figure this out.

(-1-2)^2 according to the formula should be =

1 + 4 - 4 = 1

But the answer is 9.

Where am I wrong?

Find the value of $lim x \to \infty \frac{8 - \frac{3}{x} + \frac{5}{x^{2}}}{4 + \frac{2}{x} + \frac{12}{x^{2}}}$

lim x \to 1 [\frac{3}{x^{2} + x - 2} - \frac{4}{x^{2} + 2 x - 3}]

lim x \to \infty \frac{1}{1 + x^{2}} + \frac{2}{4 + x^{2}} + \frac{3}{9 + x^{2}} + \dots + \frac{x}{x^{2} + x^{2}}

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