Solve- lim x- 1 x 4 - 3x 3 -2 x 3 - 5x 2 -3x-1

lim_x→ 1x^4 3x^2+2x^3 5x^2+3x+1 On differentiating numerator amp; denominator we get lim_x→ 1d/dx(x^4 3x^3+2)d/dx(x^3 5x^2+3x+1)=lim_x→ 14x^3 9x^23x ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

Solve: lim x...

Question

Solve:
${lim}_{x \to 1} \frac{x^{4} - {3 x}^{3} + 2}{x^{3} - {5 x}^{2} + 3 x + 1}$

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Solution

$lim x \to 1 \frac{x^{4} - 3 x^{2} + 2}{x^{3} - 5 x^{2} + 3 x + 1}$
On differentiating numerator & denominator we get
$lim x \to 1 \frac{d / d x (x^{4} - 3 x^{3} + 2)}{d / d x (x^{3} - 5 x^{2} + 3 x + 1)} = lim x \to 1 \frac{4 x^{3} - 9 x^{2}}{3 x^{2} - 10 x + 3}$
$lim x \to 1 \frac{4 x^{3} - 9 x^{2}}{3 x^{2} - 10 x + 3}$
on putting limit we get
$\frac{4 \times 1 - 9 \times 1}{3 \times 1 - 10 \times 1 + 3} = \frac{4 - 9}{3 + 3 - 10} = \frac{- 5}{- 4} = \frac{5}{4}$ .

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Solve:limx→1x4−3x3+2x3−5x2+3x+1

limx→1x4−3x2+2x3−5x2+3x+1On differentiating numerator & denominator we getlimx→1d/dx(x4−3x3+2)d/dx(x3−5x2+3x+1)=limx→14x3−9x23x2−10x+3limx→14x3−9x23x2−10x+3on putting limit we get4×1−9×13×1−10×1+3=4−93+3−10=−5−4=54.

Solve:
${lim}_{x \to 1} \frac{x^{4} - {3 x}^{3} + 2}{x^{3} - {5 x}^{2} + 3 x + 1}$