No limit for a problem on limit

Calculus Level 1

Find lim ⁡ x → ∞ x 2 + 1 − ( x 3 + 1 ) 1 3 ( x 4 + 1 ) 1 4 − ( x 4 + 1 ) 1 5 + 1 \lim_{x \to \infty} \frac{ \sqrt{ x^{2} +1} - (x^{3} +1)^{ \frac{1}{3} } }{ (x^{4} +1)^{ \frac{1}{4} } -(x^{4} +1)^{\frac{1}{5} } } +1


The answer is 1.

Sayan Chaudhuri by Sayan Chaudhuri , 23, India

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1 solution

Soumyadeep Bose
Apr 3, 2014

Take 'x' common from both numerator and denominator. then the resultant fraction appears such,that when we put the limiting value,then value of numerator becomes 0,but that of denominator becomes 1-0=1,hence the answer comes out to be (0/1)+1=1

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