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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 7 of 72
Marks: +1, -0
lim⁡x→23x2−x−10x2−4\lim\limits_{x\rightarrow 2}\frac{3x^2-x-10}{x^2-4}
Solution:  
We have, lim⁡x→23x2−x−10x2−4\lim\limits_{x\rightarrow 2}\frac{3x^2-x-10}{x^2-4} (0/0 form) = lim⁡x→2[3x2−6x+5x−10](x−2)(x+2)\lim\limits_{x\rightarrow 2}\frac{\left[3x^2-6x+5x-10\right]}{(x-2)(x+2)}
= lim⁡x→2[3x(x−2)+5(x−2)](x−2)(x+2)\lim\limits_{x\rightarrow 2}\frac{\left[3x(x-2)+5(x-2)\right]}{(x-2)(x+2)} = lim⁡x→2(3x+5)(x−2)(x−2)(x+2)\lim\limits_{x\rightarrow 2}\frac{(3x+5)(x-2)}{(x-2)(x+2)} = lim⁡x→23x+5x+2\lim\limits_{x\rightarrow 2}\frac{3x+5}{x+2}
= 3(2)+52+2\frac{3(2)+5}{2+2} = 6+54\frac{6+5}{4} = 114\frac{11}{4}.
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