Delhi University MCA 2021 Previous Year Questions (PYQs) – Page 1 of 4
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If $$ f(x) = \begin{cases} \dfrac{1}{|x|}, & |x| > 2 \\ A + Bx^2, & |x| \leq 2 \end{cases} $$ Then $f(x)$ is differentiable at $x = -2$ for
(a) A = $\tfrac{3}{4}$ ,B = $-\tfrac{1}{16}$
(b) A = $-\tfrac{3}{4}$ , B = $\tfrac{1}{16}$
(c) A = $-\tfrac{3}{4}$ ,B = $-\tfrac{1}{16}$
(d) A = $\tfrac{3}{4}$, B = $\tfrac{1}{16}$
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Solution
$$ S_n = \left[ (n+1)(n+2)\cdots(n+n)\cdot \frac{1}{n^n} \right]^{\tfrac{1}{n}} $$
$$ \lim_{n \to \infty} S_n = \; ? $$
$$ (a)\;\tfrac{1}{e} \qquad (b)\;\tfrac{2}{e} \qquad (c)\;\tfrac{4}{e} \qquad (d)\;1 $$
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Solution
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