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Limits Continuity and Differentiability · 2022 · Shift 2

2 Mathematics questions from this JEE Advanced paper

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JEE Advanced
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2022 · Shift 2
Mathematics
Limits Continuity and Differentiability

Limits Continuity and Differentiability · 2022 · Shift 2

2 Mathematics questions from this JEE Advanced paper

Q23.If $β = x \to 0 lim \frac{e ^{x^{3}} - ( 1 - x ^{3} ) ^{\frac{1}{3}} + ( ( 1 - x ^{2} ) ^{\frac{1}{2}} - 1 ) s i n x}{x s i n ^{2} x},$ then the value of $6 β$ is .
Mathematics · Limits Continuity and Differentiability · Numerical
Q36.For positive integer $n$ , define $f (n) = n + \frac{16 + 5 n - 3 n ^{2}}{4 n + 3 n ^{2}} + \frac{32 + n - 3 n ^{2}}{8 n + 3 n ^{2}} + \frac{48 - 3 n - 3 n ^{2}}{12 n + 3 n ^{2}} + \dots + \frac{25 n - 7 n ^{2}}{7 n ^{2}} .$ Then, the value of $n \to \infty lim f (n)$ …
Mathematics · Limits Continuity and Differentiability · MCQ