\lim_{x\to0}\sqrt{1+x^3}-\sqrt{1-x^2}/x^2 =

AP ICET 2019 Shift 2 Paper

Question : 134 of 200

Marks: +1, -0

\lim↙{x→0}{√{1+x^3}-√{1-x^2}}/x^2

Solution:

\lim ↙{x → 0} \;{(1+x^{3})-(1-x^{2})}/{x^{2}(√{1+x^{3}}+√{1-x^{2}})}

\lim ↙{x → 0}=\;{x^{2}(x+1)}/{x^{2}(√{1+x^{3}}+√{1-x^{2}})}=\;{1}/{2}

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