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Question : 63 of 160
Marks:
+1,
-0
Solution:
y=√‌| x4√3x−5 |
| (x2−3)(2x−3) |
Take the natural
log to both sides, we get
‌ln(y)=‌‌ln(‌| x4√3x−5 |
| (x2−3)(2x−3) |
)‌ln(y)=‌[ln(x4)+ln(√3x−5)−ln(x2−3)−ln(2x−3)]‌=‌[4‌ln(x)+‌‌ln(3x−5)−ln(x2−3)−ln(2x−3)]Now, differentiating w.r.t
x, we get
‌‌⋅‌=‌[‌+‌⋅‌−‌−‌]‌‌=‌[‌+‌−‌−‌]Now, at
x=2y=√‌| 24√3⋅2−5 |
| (22−3)(4−3) |
=√‌=4So,
‌‌‌|x=2=‌[‌+‌−‌−‌]‌=2[2+‌−‌−2]=2[‌]=−5‌∴‌‌‌|x=2=−5
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