The value of limx- 2x3-6x2-11x-6x2-6x-8 is

Lim_x→ 2x^3 6x^2+11x 6x^2 6x+8 This is a 0 0 form, using factorisation, we get lim_x→ 2x^3 6x^2+11x 6x^2 6x+8 nbsp;=lim_x→ 2(x 2)(x^2 4x+3)(x 2)(x 4) nbsp ...

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Byju's Answer

Standard XII

Mathematics

Property 7

The value of ...

Question

The value of $lim x \to 2 \frac{x^{3} - 6 x^{2} + 11 x - 6}{x^{2} - 6 x + 8}$ is

2

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- 2

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\frac{1}{2}

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Limit doesn't exists.

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Solution

The correct option is C $\frac{1}{2}$
$lim x \to 2 \frac{x^{3} - 6 x^{2} + 11 x - 6}{x^{2} - 6 x + 8}$
This is a $\frac{0}{0}$ form, using factorisation, we get
$lim x \to 2 \frac{x^{3} - 6 x^{2} + 11 x - 6}{x^{2} - 6 x + 8} = lim x \to 2 \frac{(x - 2) (x^{2} - 4 x + 3)}{(x - 2) (x - 4)} = lim x \to 2 \frac{x^{2} - 4 x + 3}{x - 4} = \frac{4 - 8 + 3}{- 2} = \frac{1}{2}$

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Similar questions

Q. Solve

{lim}_{x \to 2} \frac{x^{3} - 6 x^{2} + 11 x - 6}{x^{2} - 6 x + 8}

Q. Evaluate :

{lim}_{x \to 2} \frac{x^{3} - 6 x^{2} + 11 x - 6}{x^{2} - 6 x + 8}

Q. f(x) = x³ − 6x² + 11x − 6, g(x) = x² − 3x + 2

Q. The values of

a

for which

\frac{x^{3} - 6 x^{2} + 11 x - 6}{x^{3} + x^{2} - 10 x + 8} + \frac{a}{30} = 0

does not have a real solution is

Q. Divide

x^{3} - 6 x^{2} + 11 x - 6

x^{2} + x + 1

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Property 7

Standard XII Mathematics

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The value of limx→2x3−6x2+11x−6x2−6x+8 is

The correct option is C 12limx→2x3−6x2+11x−6x2−6x+8 This is a 00 form, using factorisation, we get limx→2x3−6x2+11x−6x2−6x+8=limx→2(x−2)(x2−4x+3)(x−2)(x−4)=limx→2x2−4x+3x−4=4−8+3−2=12

The value of $lim x \to 2 \frac{x^{3} - 6 x^{2} + 11 x - 6}{x^{2} - 6 x + 8}$ is