જો $l_1 = \lim_{x \rightarrow 2^{+}} (x + [x])$,$l_2 = \lim_{x \rightarrow 2^{-}} (2x - [x])$ અને $l_3 = \lim_{x \rightarrow \pi/2} \frac{\cos x}{x - \pi/2}$ હોય,તો:

  • A
    $l_1 < l_2 < l_3$
  • B
    $l_2 < l_3 < l_1$
  • C
    $l_3 < l_2 < l_1$
  • D
    $l_1 < l_3 < l_2$

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લક્ષની કિંમત શોધો: $\lim _{x \rightarrow 0^{+}}\left(e^{x}+x\right)^{1 / x}$

જો $\alpha = \lim_{x \rightarrow 0} \frac{x \cdot 2^x - x}{1 - \cos x}$ અને $\beta = \lim_{x \rightarrow 0} \frac{x \cdot 2^x - x}{\sqrt{1+x^2} - \sqrt{1-x^2}}$,હોય તો

ધારો કે $f(x) = x^{6} + 2x^{4} + x^{3} + 2x + 3$,$x \in R$. તો પ્રાકૃતિક સંખ્યા $n$ શોધો જેના માટે $\lim_{x \rightarrow 1} \frac{x^{n} f(1) - f(x)}{x - 1} = 44$ થાય.

$\mathop {\lim }\limits_{x \to \infty } \frac{{\log x}}{{{x^n}}}, \; n > 0$ ની કિંમત શું છે?

$\mathop {\lim }\limits_{x \to 0} \,\frac{{{e^x} - x - 1}}{{{x^2}}}$ ની કિંમત શોધો.

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