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Question

Mathematics Question on Limits

Evaluate the Given limit: lim⁡x→2\lim_{x\rightarrow 2} 3x2−x−10x2−4\frac{3x^2-x-10}{x^2-4}

Answer

At x = 2, the value of the given rational function takes the form 0/0
lim⁡x→2\lim_{x\rightarrow 2} 3x2−x−10x2−4\frac{3x^2-x-10}{x^2-4} =lim⁡x→2\lim_{x\rightarrow 2} (x−2)(3x+5)(x−2)(x+2)\frac{(x-2)(3x+5)}{(x-2)(x+2)}
lim⁡x→2\lim_{x\rightarrow 2} 3x+5x+2\frac{3x+5}{x+2}
=3(2)+52+2\frac{3(2)+5}{2+2}
=114\frac{11}{4}