Question:

Evaluate the Given limit: limx3\lim_{x\rightarrow 3} x4812x25x3\frac{x^4-81}{2x^2-5x-3}

Updated On: Oct 23, 2023
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Solution and Explanation

At x=2, the value of the given rational function takes the form 0/0 
=limx3\lim_{x\rightarrow 3} (x3)(x+3)(x2+9)(x3)(2x+1)\frac{(x-3)(x+3)(x^2+9)}{(x-3)(2x+1)}
=limx3\lim_{x\rightarrow 3} (x+3)(x2+9)2x+1\frac{(x+3)(x^2+9)}{2x+1}
=(3+3)(32+9)2(3)+1\frac{(3+3)(32+9)}{2(3)+1}
=6×187\frac{6\times 18}{7}
=1087\frac{108}{7}
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