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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
| LIST I | LIST II | ||
|---|---|---|---|
| A. | $\displaystyle \lim_{x\to0}\left(\dfrac{\sin x}{x}\right)^{\frac{\sin x}{x-\sin x}}$ | I. | $e^3$ |
| B. | $\displaystyle \lim_{x\to0}\dfrac{\int_0^x \sin^2 t\,dt}{x^2}$ | II. | $0$ |
| C. | $\displaystyle \lim_{x\to0}(e^{2x}+x)^{1/x}$ | III. | $1$ |
| D. | $\displaystyle \lim_{x\to a}\dfrac{\log(x-a)}{e^x-e^a}$ | IV. | $e^{-1}$ |
Solution
A: Standard limit → $e^{-1}$ → IV
B: $\int_0^x \sin^2 t,dt \sim \dfrac{x^3}{3}$ ⇒ limit $=0$ → II
C: $(e^{2x}+x)^{1/x} \to e^3$ → I
D: Using L’Hospital ⇒ limit $=1$ → III
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