Evaluate the limit-limx - 2x2 -x-2x2 -2x - sinx-2

We have: nbsp; lim_x → 2x^2 x 2x^2 2x + sin(x 2) =lim_x → 2((x 2)(x+1))((x(x 2))+ sin (x 2)) =lim_x → 2(x+1)( x+ sin (x 2)x 2 ) Dividing numerator and de ...

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Standard XII

Mathematics

Expansions to Remove Indeterminate Form

Evaluate the ...

Question

Evaluate the limit:
$lim x \to 2 \frac{x^{2} - x - 2}{x^{2} - 2 x + sin (x - 2)}$

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Solution

We have:
$lim x \to 2 \frac{x^{2} - x - 2}{x^{2} - 2 x + sin (x - 2)}$

$= lim x \to 2 \frac{((x - 2) (x + 1))}{((x (x - 2)) + sin (x - 2))}$

$= lim x \to 2 \frac{(x + 1)}{(x + \frac{sin (x - 2)}{x - 2})}$

Dividing numerator and denominator by $(x - 2)$

$= \frac{3}{3} = 1$

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Expansions to Remove Indeterminate Form

Standard XII Mathematics

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Evaluate the limit: limx→2x2−x−2x2−2x+sin(x−2)

We have: limx→2x2−x−2x2−2x+sin(x−2) =limx→2((x−2)(x+1))((x(x−2))+sin(x−2)) =limx→2(x+1)(x+sin(x−2)x−2) Dividing numerator and denominator by (x−2) =33=1

Evaluate the limit:
$lim x \to 2 \frac{x^{2} - x - 2}{x^{2} - 2 x + sin (x - 2)}$

We have:
$lim x \to 2 \frac{x^{2} - x - 2}{x^{2} - 2 x + sin (x - 2)}$

$= lim x \to 2 \frac{((x - 2) (x + 1))}{((x (x - 2)) + sin (x - 2))}$

$= lim x \to 2 \frac{(x + 1)}{(x + \frac{sin (x - 2)}{x - 2})}$

Dividing numerator and denominator by $(x - 2)$

$= \frac{3}{3} = 1$