Lim x - 4x2-7 x-12-x2-3 x-4

Lim_x → 4x^2 7x+12/x^2 3x 4 It is of the form 0/0 =lim_x → 4x^2 3x 4x+12/x^2+x 4x 4 =lim_x → 4x(x 3) 4(x 3)/x(x+1) 1(x+1) =lim_x → 4(x 3)(x 4)/(x 4)(x+1) =lim_x ...

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Byju's Answer

Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

lim x → 4x2-7...

Question

${lim}_{x \to 4} \frac{x^{2} - 7 x + 12}{x^{2} - 3 x - 4}$

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Solution

${lim}_{x \to 4} \frac{x^{2} - 7 x + 12}{x^{2} - 3 x - 4}$

It is of the form $\frac{0}{0}$

$= {lim}_{x \to 4} \frac{x^{2} - 3 x - 4 x + 12}{x^{2} + x - 4 x - 4}$

$= {lim}_{x \to 4} \frac{x (x - 3) - 4 (x - 3)}{x (x + 1) - 1 (x + 1)}$

$= {lim}_{x \to 4} \frac{(x - 3) (x - 4)}{(x - 4) (x + 1)}$

$= {lim}_{x \to 4} \frac{x - 3}{x + 1}$

$= \frac{4 - 3}{4 + 1} = \frac{1}{5}$

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Similar questions

Q. Evaluate the following:

\begin{matrix} {lim}_{x \to 1} \frac{x^{2} - 3 x + 2}{x^{2} - 4 x + 3} {lim}_{x \to 2} \frac{x^{3} + x^{2} - 12}{x^{3} - x^{2} - x - 2} {lim}_{x \to \sqrt{2}} \frac{x^{2} + x \sqrt{2} - 4}{x^{2} - 3 x \sqrt{2} + 4} {lim}_{x \to 3} \frac{x^{3} - 3 x^{2} - x + 3}{x^{3} - 6 x^{2} + 9 x} \end{matrix}

Q. Solve the equation

\sqrt{4 x^{2} - 7 x - 15} - \sqrt{x^{2} - 3 x} = \sqrt{x^{2} - 9}

Solve:

{lim}_{x \to 4^{+}} \frac{x^{2} - 7 x + 12}{x - [x]} =

[where

[.]

denotes G.I.F]

Q. Simplify

\frac{x}{x^{2} + 3 x - 4} + \frac{4 x}{x^{2} + 7 x + 12} .

Q. Solve the following equations:

\sqrt{4 x^{2} - 7 x - 15} - \sqrt{x^{2} - 3 x} = \sqrt{x^{2} - 9}

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limx→4x2−7x+12x2−3x−4

limx→4x2−7x+12x2−3x−4 It is of the form 00 =limx→4x2−3x−4x+12x2+x−4x−4 =limx→4x(x−3)−4(x−3)x(x+1)−1(x+1) =limx→4(x−3)(x−4)(x−4)(x+1) =limx→4x−3x+1 =4−34+1=15

${lim}_{x \to 4} \frac{x^{2} - 7 x + 12}{x^{2} - 3 x - 4}$