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Show that the function f:R to R defined ...

Show that the function `f:R to R` defined by `f(x)=(x)/(x^(2)+1)` is neither one-one nor onto.

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ARIHANT PUBLICATION-SAMPLE PAPER 5-Short answer type question
  1. Show that the relation R on the set A = {1,2,3,4,5) given by R = {(a,b...

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  2. Evaluate int (x^(2) + 2x) dx.

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  3. Show that the function f:R to R defined by f(x)=(x)/(x^(2)+1) is neith...

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  4. Solve the equation sin^(-1)6x+2sin^(-1)6sqrt(3)x=(-pi)/(2).

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  5. Find the inverse of the following matrix [{:(1,1,2),(0,1,2),(1,2,1):}]...

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  6. A bag contains 5 red marbles and 3 black marbles. Three , marbles are ...

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  7. Using properties of determinants prove that |{:(a^2+2a,2a+1,1),(2a+1...

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  8. A and B throw a pair of dice alternately. A wins the game, if he gets ...

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  9. If A=[{:(1,5),(7,12):}] and B=[{:(9,1),(7,8):}], find a matrix C such ...

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  10. Find the derivative of cos^(-1)((sin x +cos x)/(sqrt(2))),(-pi)/(4)lt ...

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  11. If x=e^(x//y), prove that (dy)/(dx)=(x-y)/(xlogx).

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  12. Find the condition that curves 2x = y^(2) and 2xy = k intersect ortho...

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  13. Evaluate int(1)^(3) (3x^(2) + 2x+1) dx .

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  14. Examine the differentiability of the function f defined by f(x)={{:(2x...

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  15. Evaluate intsqrt((1+x)/(1-x))dx, x ne 1

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  16. Solve the following differential equation x^(2).(dy)/(dx)-xy=1+cos((...

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  17. Find the area of region enclosed by the curve x=3cost, y=2sint.

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  18. int0^(pi/2) (sin^2xdx)/(sinx+cosx)

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  19. Form the differential equation having y= (sin^(-1)x)^(2)+A cos^(-1)x+B...

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  20. The two vectors hatj+hatk and 3hati+hatj+4hatk represents the two side...

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