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Vivek Bhardwaj Grade: 12
        

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 given if possible.


Regards,


Vivek

7 years ago

Answers : (1)

Nehal Wani
21 Points
										

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

7 years ago
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