Question

Limit xtens to 0 x^2logx^2 what is the ans of interminate forms?

Answer 1

Rewrite the limit as

`\displaystyle\lim_(x\to0)x^2\log x^2=\lim_(x\to0)\frac{\log x^2}{\frac1{x^2}}`

Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get

`\displaystyle\lim_(x\to0)\frac{\log x^2}{\frac1{x^2}}=\lim_(x\to0)\frac{\frac2x}{-\frac2{x^3}}=\lim_(x\to0)-x^2=\boxed{0}`