GATE (TF) Textile 2010 Question Paper Solution | GATE/2010/TF/46

Question 46 (Textile Engineering & Fibre Science)

When x\rightarrow 4, \lim \frac{x^3-64}{log_e(x-3)} will be equal to

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x\rightarrow 4 , \lim \frac{x^3-64}{log_e(x-3)}

We will expand the log(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}-.........

x\rightarrow 4 , \lim \frac{(x-4)(x^2+16+4x)}{(x-4)-\frac{(x-4)^2}{2}+\frac{(x-4)^3}{3}+......}

x\rightarrow 4 , \lim \frac{(x^2+16+4x)}{1-\frac{(x-4)}{2}+\frac{(x-4)^2}{3}+......}

By taking limit-

\frac{(4^2+16+4\times 4)}{1-\frac{(4-4)}{2}+\frac{(4-4)^2}{3}+......}


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