Evaluate the limit-limx-3x2-9 1x-3-1x-3

Given: nbsp;lim_x→3(x^2 9)( 1/x+3+1/x 3) Using Factorization method lim_x→3(x^2 9)( 1x+3+1x 3) (0×∞ ) form lim_x→3,(x^2 9)( 1x+3 1x 3) lim_x→3(x^2 9)( (x ...

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Standard XII

Mathematics

Single Point Continuity

Evaluate the ...

Question

Evaluate the limit:
$lim x \to 3 (x^{2} - 9) (\frac{1}{x + 3} + \frac{1}{x - 3})$

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Solution

Given: $lim x \to 3 (x^{2} - 9) (\frac{1}{x + 3} + \frac{1}{x - 3})$

Using Factorization method
$lim x \to 3 (x^{2} - 9) (\frac{1}{x + 3} + \frac{1}{x - 3})$

$(0 \times \infty) f o r m$

$lim x \to 3, (x^{2} - 9) (\frac{1}{x + 3} - \frac{1}{x - 3})$

$lim x \to 3 (x^{2} - 9) (\frac{(x - 3) + (x + 3)}{(x + 3) (x - 3)})$

$\Rightarrow lim x \to 3 (x^{2} - 9) (\frac{2 x}{x^{2} - 9})$

$\Rightarrow lim x \to 3 (2 x)$

$= 2 \times 3 = 6$

$T h e r e f o r e,$

$\Rightarrow lim x \to 3 (x^{2} - 9) (\frac{1}{x + 3} + \frac{1}{x - 3}) = 6$

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Single Point Continuity

Standard XII Mathematics

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Evaluate the limit: limx→3(x2−9)(1x+3+1x−3)

Given: limx→3(x2−9)(1x+3+1x−3) Using Factorization method limx→3(x2−9)(1x+3+1x−3) (0×∞)form limx→3,(x2−9)(1x+3−1x−3) limx→3(x2−9)((x−3)+(x+3)(x+3)(x−3)) ⇒limx→3(x2−9)(2xx2−9) ⇒limx→3(2x) =2×3=6 Therefore, ⇒limx→3(x2−9)(1x+3+1x−3)=6

Evaluate the limit:
$lim x \to 3 (x^{2} - 9) (\frac{1}{x + 3} + \frac{1}{x - 3})$