Question

${ \boxed { \boxed{\huge \red{\bold{{ \displaystyle{ \lim_{x \to \infty}}} \sqrt[x]{x}}}}}}$


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❖ᴏɴʟʏ ᴘʀᴏᴘᴇʀ ꜱᴏʟᴠᴇᴅ ᴀɴꜱᴡᴇʀ ᴡɪᴛʜ ɢᴏᴏᴅ ᴇxᴘʟᴀɴᴀɪᴏɴ ɴᴇᴇᴅᴇᴅ
❖ ɴᴏ ꜱᴘᴀᴍᴍɪɴɢ
❖ᴏɴʟʏ ꜰᴏʀ ᴍᴏᴅᴇʀᴀᴛᴏʀꜱ, ʙʀᴀɪɴʟʏ ꜱᴛᴀʀꜱ ᴀɴᴅ ᴏᴛʜᴇʀ ʙᴇꜱᴛ ᴜꜱᴇʀꜱ​​​​​​

Answer 1

$\bold{{ \displaystyle{ \lim_{x \to \infty}}} \sqrt[x]{x}}$

$= \bold{{ \displaystyle{ \lim_{x \to \infty}}}}x {}^{ \frac{1}{x} }$

$= \bold{{{ \displaystyle{ \lim_{x \to \infty}}}}e {}^{ \frac{1}{x} \times \: Inx}}$

$\bold{ =e \displaystyle{ \lim_{x \to \infty}}}\bold{\dfrac{ \frac{1}{x} }{1}}$

$\bold{ = e {}^{0} = 1}$