જો mathop {lim }limits_{x to frac{1}{2}} frac | vedclass

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(D) આપેલ છે કે $\mathop {\lim }\limits_{x 	o \frac{1}{2}} \frac{{a{x^2} + bx + c}}{{{{\left( {2x - 1} ight)}^2}}} = \frac{1}{2}$.અહીં $a{x^2} + bx

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(D) આપેલ છે કે $\mathop {\lim }\limits_{x 	o \frac{1}{2}} \frac{{a{x^2} + bx + c}}{{{{\left( {2x - 1} ight)}^2}}} = \frac{1}{2}$.અહીં $a{x^2} + bx + c = \frac{1}{2}(2x - 1)^2 = 2x^2 - 2x + \frac{1}{2}$ મળે છે.તેથી,$a = 2, b = -2, c = \frac{1}{2}$.હવે,$\mathop {\lim }\limits_{x 	o 2} \frac{{(x - 2)(x + 2)(x - \frac{1}{2})}}{{x - 2}}$ ની ગણતરી કરતા,$= (2 + 2)(2 - \frac{1}{2}) = 4 	imes \frac{3}{2} = 6$.

જો $\mathop {\lim }\limits_{x \to \frac{1}{2}} \frac{{a{x^2} + bx + c}}{{{{(2x - 1)}^2}}} = \frac{1}{2}$ હોય,તો $\mathop {\lim }\limits_{x \to 2} \frac{{(x - a)(x - b)(x - c)}}{{x - 2}}$ ની કિંમત શોધો.

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