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1. Find the set of Points where the function of f(x)=tan[∏2]x-tan[-∏2]x
2. Let a real function f is given by f(x) =n(x1/n-1), x>0. If f(x) satisfies 97f(1/x)+Kf(x)=0, then find the value of K
Solution to the above two problems may pl be give?n? ?i?f? ?p?o?s?s?i?b?l?e?.
?Regards,?
?Vivek??
If 5f(x)+3f(1/x)=x+2 and y=xf(x), then dy/dx at x=1
5f(x)+3f(1/x)=x+2
25f(x)+15(1/x)=5x+10…………………..(i)
Replacing x with 1/x,
5f(1/x)+3(x)=1/x+2
15f(1/x)+9f(x)=3/x+6………………………(ii)
(i)-(ii)
16f(x)=5x-3/x+4
f(x)=5x/16-3/16x+1/4
y=xf(x)=5x2/16-3/16+x/4
dy/dx=10x/16+1/4
dy/dx at x=1 is 10/16+1/4=7/8
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