Question

x limit X tends to 2 X square + X - 6 by x minus 2 is equals​

Answer 1

lim (x² + x - 6)/x - 2

x→2

On putting x = 2, we see that this equation is in indeterminant form. Thus, we first carry on certain operations which actually don't change the value of the equation, but it doesn't result in indeterminant form.

Simplification of equation:

» (x² + x - 6)/x - 2

» (x² + 3x - 2x - 6)/x - 2

» (x + 3)(x - 2)/(x - 2)

» x + 3

Now, put x = 2:

x + 3 = 2 + 3 = 5

Answer 2

SOLUTION

TO EVALUATE

$\displaystyle \sf \lim_{x \to 2} \: \frac{ {x}^{2} + x - 6 }{x-2}$

EVALUATION

Here the given limit is

$\displaystyle \sf \lim_{x \to 2} \: \frac{ {x}^{2} + x - 6 }{x-2}$

We solve it using L'HOSPITAL RULE

$\displaystyle \sf \lim_{x \to 2} \: \frac{ {x}^{2} + x - 6 }{x-2} \: \: \: \bigg( \frac{0}{0} \: \: form\bigg)$

$\displaystyle \sf = \lim_{x \to 2} \: \frac{ 2x+ 1 }{1}$

$\displaystyle \sf = \lim_{x \to 2} \: (2x+ 1)$

$\displaystyle \sf = (2 \times 2) + 1$

$\displaystyle \sf =4 + 1$

$\displaystyle \sf = 5$

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