mathop {lim }limits_{x to infty } {left[ {1 + | vedclass

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Question

(A) ધારો કે $y = \mathop {\lim }\limits_{x 	o \infty } {\left( {1 + \frac{1}{{mx}}} ight)^x}$.આપણે પદાવલિને $y = \mathop {\lim }\limits_{x 	o \inf

Vedclass · Accepted Answer

$e^{1/m}$

Vedclass · Answer

(A) ધારો કે $y = \mathop {\lim }\limits_{x 	o \infty } {\left( {1 + \frac{1}{{mx}}} ight)^x}$.આપણે પદાવલિને $y = \mathop {\lim }\limits_{x 	o \infty } {\left[ {\left( {1 + \frac{1}{{mx}}} ight)^{mx}} ight]^{1/m}}$ તરીકે લખી શકીએ.પ્રમાણિત લક્ષના સૂત્ર $\mathop {\lim }\limits_{u 	o \infty } {\left( {1 + \frac{1}{u}} ight)^u} = e$ નો ઉપયોગ કરતા,જ્યાં $u = mx$,જેમ $x 	o \infty$,તેમ $u 	o \infty$.તેથી,$y = e^{1/m}$.

$\mathop {\lim }\limits_{x \to \infty } {\left[ {1 + \frac{1}{{mx}}} \right]^x}$ ની કિંમત શોધો.

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