Lim x -2 x4 -4x2 - 3x-2 - 8

L=lim_x √(2)x^4/x^2+4√(2)x √(2)x 8=x^4 4/x(x+4√(2)) √(2)(x+4√(2)) =x^4 4/(x √(2))(x+4√(2))=(x^2 2)(x^2+2)/(x √(2))(x+4√(2))=(x+√(2))(x^2+2)/x+4√(2) ...

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Byju's Answer

Standard VII

Mathematics

Comparison of Fractions

lim x →√2 x...

Question

$lim x \to \sqrt{2}$ $\frac{x^{4} - 4}{x^{2} + 3 x \sqrt{2} - 8}$

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Solution

$L = {lim}_{x - \sqrt{2}} \frac{x^{4}}{x^{2} + 4 \sqrt{2} x - \sqrt{2} x - 8} = \frac{x^{4} - 4}{x (x + 4 \sqrt{2}) - \sqrt{2} (x + 4 \sqrt{2})}$
$= \frac{x^{4} - 4}{(x - \sqrt{2}) (x + 4 \sqrt{2})} = \frac{(x^{2} - 2) (x^{2} + 2)}{(x - \sqrt{2}) (x + 4 \sqrt{2})} = \frac{(x + \sqrt{2}) (x^{2} + 2)}{x + 4 \sqrt{2}}$
$= \frac{(\sqrt{2} + \sqrt{2}) (2 + 3)}{\sqrt{2} + 4 \sqrt{2}} = \frac{4 \times 2 \sqrt{2}}{5 \sqrt{2}} = \frac{8}{5}$

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limx→√2 x4−4x2+3x√2−8

L=limx−√2x4x2+4√2x−√2x−8=x4−4x(x+4√2)−√2(x+4√2)=x4−4(x−√2)(x+4√2)=(x2−2)(x2+2)(x−√2)(x+4√2)=(x+√2)(x2+2)x+4√2=(√2+√2)(2+3)√2+4√2=4×2√25√2=85

$lim x \to \sqrt{2}$ $\frac{x^{4} - 4}{x^{2} + 3 x \sqrt{2} - 8}$