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If :f(x)=log((1+x)/(1-x)),then show that...

If :`f(x)`=log`((1+x)/(1-x)),`then show that f(a)+f(b)=f`((a+b)/(1+ab))`and 2f(x)=f`((2x)/(1+x^2)).`

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USHA PUBLICATION-RELATION AND FUNCTION INVERSE TRIGONOMETRIC FUNCTIONS LINEAR PROGRAMMING-EXERCISE
  1. Find the feasible region of the inequations x+2ylt8, 2x+ylt8 and xgt0,...

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  2. Find the feasible region of the inequations 2x1+4x2gt40, 3x1+2x2gt60, ...

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  3. Shade the feasible region satisfying ineuations x1+2x2ge10, 2x1+2x2ge1...

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  4. Shade the feasible region satisfying ineuations x+2yle10, x+yge1, x-yl...

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  5. Shade the feasible region satisfying ineuations 4x+3yle60, 2x-yle0, x-...

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  6. Prove that the following sets A,B,C D are equivalent. WhereA={1,2,3,4,...

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  7. Let n be a positive integer,and a function f be defined as follows:{(0...

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  8. Let f be an invertible function . Then prove that (f^(-1))^(-1) = f.

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  9. If P(A/B) gt P(A) then prove that P(B/A) gt P(B)

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  10. If :f(x)=log((1+x)/(1-x)),then show that f(a)+f(b)=f((a+b)/(1+ab))and ...

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  11. If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)...

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  12. If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)...

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  13. Solve:Sin^-1x+sin^-1(1-x)=cos^1x

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  14. Solve sin^(-1)x +sin^(-1)(1-x) =(pi)/(2).

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  15. If: tan (pi cos""theta/2)=cot(pisin"theta/2),then show thattheta=sin^1...

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  16. Maximize Z=6x1+10x2subject to x1+2x2gt10,2x1+2x2gt12,3x1+x2gt8,x1,x2gt...

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  17. Solve graphically 4x+7yle28

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  18. Let an LPP be as follows: Maximize Z=3x1+5x2 subject to x1+2x2le12, 2x...

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  19. 11.Minimize Z=20x1+40x2subject to the constraints36x1+6x2ge108,3x1+12x...

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  20. Solve the following LPP graphically Maximizez=20x+10y Subject to x+2...

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