Evaluate the following limit-lim x - 3x4-81-2 x2-5 x-3

Here, x → 3limx^4 81/2x^2 5x 3 [ 0/0 form] = x → 3lim(x^2+9)(x+3)(x 3)/(x 3)(2x+1) = x → 3lim(x^2+9)(x+3)/(2x+1) = (3^2+9)(3+3)/(2 × 3 + 1) = 108/7 ...

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Byju's Answer

Standard XII

Mathematics

Existence of Limit

Evaluate the ...

Question

Evaluate the following limit:

$lim x \to 3 \frac{x^{4} - 81}{2 x^{2} - 5 x - 3}$

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Solution

Here,
$lim x \to 3 \frac{x^{4} - 81}{2 x^{2} - 5 x - 3} [\frac{0}{0} form]$

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

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

= $\frac{(3^{2} + 9) (3 + 3)}{(2 \times 3 + 1)} = \frac{108}{7}$

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Evaluate the following limit: limx→3x4−812x2−5x−3

Here, limx→3x4−812x2−5x−3[00 form] = limx→3(x2+9)(x+3)(x−3)(x−3)(2x+1) = limx→3(x2+9)(x+3)(2x+1) = (32+9)(3+3)(2×3+1)=1087

Evaluate the following limit:

$lim x \to 3 \frac{x^{4} - 81}{2 x^{2} - 5 x - 3}$

Here,
$lim x \to 3 \frac{x^{4} - 81}{2 x^{2} - 5 x - 3} [\frac{0}{0} form]$

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

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

= $\frac{(3^{2} + 9) (3 + 3)}{(2 \times 3 + 1)} = \frac{108}{7}$