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1.Find the set of Points where the function of f(x)=tan[∏ 2 ]x-tan[-∏ 2] x 2. If 5f(x)+3f(1/x)=x+2 and y=xf(x), then dy/dx at x=1 3. Let a real function f is given by f(x) =n(x 1/n -1), x>0. If f(x) satisfies 97f(1/x)+Kf(x)=0, then find the value of K

1.Find the set of Points where the function of f(x)=tan[∏2]x-tan[-∏2]x


2. If 5f(x)+3f(1/x)=x+2 and y=xf(x), then dy/dx at x=1


3. 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

Grade:12

1 Answers

Nehal Wani
21 Points
10 years ago

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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