Question

ǫᴜᴇsᴛɪᴏɴ ( ᴊᴇᴇ ) ❤ :

sᴏʟᴠᴇ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ ᴏғ ᴀᴛᴛᴀᴄʜᴍᴇɴᴛ ^_^ ...

✫ ᴄᴏɴᴛᴇɴᴛ ǫᴜᴀʟɪᴛʏ ʀᴇǫᴜɪʀᴇᴅ ✫

ᴛʜᴀɴᴋs :)
ᴀʟʟ ᴛʜᴇ ʙᴇsᴛ ❤ .​

Answer 1

Answer

$\rm \lim_{x\to 0}\dfrac{f(x^2)-f(x)}{f(x)-f(0)}\\\\\rm Apply\ L-Hospital's\ rule\\\\\to \rm \lim_{x\to 0}\dfrac{f'(x^2)(2x)-f'(x)}{f'(x)-0}\\\\\to \rm \lim_{x\to 0}\dfrac{2x.f'(x^2)-f'(x)}{f'(x)}\\\\\to \rm \left( \dfrac{2(0)f'(0^2)-f'(0)}{f'(0)}\right)\\\\\to \rm \left(\dfrac{0-f'(0)}{f'(0)}\right)\\\\\to \rm -\left(\dfrac{f'(0)}{f'(0)}\right)\\\\\to \rm -1\ \; \pink{\bigstar}$

So , $\orange{\bigstar}$ Option C $\green{\bigstar}$ is correct