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Question : 124 of 150
Marks:
+1,
-0
Solution:
√x2+y2=atan−1(‌) . . . (i)
Putting
x=0, we get
‌y=atan−1(∞)‌y=‌Now, differentiating Eq. (i) w.r.t. x, we get
‌‌=a⋅‌⋅{‌}‌⇒‌=‌{‌}‌⇒√x2+y2(x+y‌)=a(x‌−y)...(ii)‌‌ At ‌x=0,y=‌,‌‌[‌⋅‌]=a[−‌]‌‌⋅‌=−1‌‌=−‌Again, differentiating Eq. (ii), w.r.t.
x, we get
‌⋅(x+y‌)+√x2+y2[1+y‌+(‌)2]=a[x‌+‌−‌]⇒‌+√x2+y2[1+y‌+(‌)2]=ax‌Putting
x=0,y=‌,‌=−‌‌(−‌)2+‌[1+‌(‌)+(−‌)2]=0⇒‌‌‌+‌+‌⋅‌+‌⋅‌=0⇒‌‌‌+‌+‌⋅‌=0 ⇒‌‌‌+‌+‌⋅‌=0⇒‌‌‌=‌=‌
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