cmi-entrance 2022 QA6

cmi-entrance · India · ugmath_22may 4 marks Curve Sketching Multi-Statement Verification (Remarks/Options)

Let $$f(x) = \frac{1}{|\ln x|}\left(\frac{1}{x} + \cos x\right)$$
Statements
(21) As $x \rightarrow \infty$, the sign of $f(x)$ changes infinitely many times. (22) As $x \rightarrow \infty$, the limit of $f(x)$ does not exist. (23) As $x \rightarrow 1$, $f(x) \rightarrow \infty$. (24) As $x \rightarrow 0^+$, $f(x) \rightarrow 1$.

Let
$$f(x) = \frac{1}{|\ln x|}\left(\frac{1}{x} + \cos x\right)$$

Statements

(21) As $x \rightarrow \infty$, the sign of $f(x)$ changes infinitely many times.\\
(22) As $x \rightarrow \infty$, the limit of $f(x)$ does not exist.\\
(23) As $x \rightarrow 1$, $f(x) \rightarrow \infty$.\\
(24) As $x \rightarrow 0^+$, $f(x) \rightarrow 1$.

Paper Questions

QA1 QA10 QA2 QA3 QA4 QA5 QA6 QA7 QA8 QA9 QB1 QB2 QB3 QB4 QB5 QB6