Q41 / 90 · NTA Abhyas (JEE Main) 2020 · Mathematics · Limits

The value oflimx→1+∫1xt-1dtsin⁡(x-1) is equal to

Correct answer: 0

Solution

Given: lim x→ 1 + ∫ 1 x (t−1) dt sin(x−1)

Using L’Hospital’s rule and leibuitzrule,

l= lim x→ 1 + d dx ∫ 1 x (t−1) dt d dx sin x−1

lim x→ 1 + x−1 cos x−1 = 0 1 =0

Hence, the correct answer is 0.

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