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Prove that the function f(x) = x+1/x(x!=...

Prove that the function `f(x) = x+1/x(x!=0)` is decreasing for all x in `(-1,0)uu(0,1)`.

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UNITED BOOK HOUSE-SET 2-EXERCISE
  1. Evaluate: overset(2)underset(1)int logx dx

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  2. Find the order of the differential equation ((d^4y)/(dx^4))^3-(d^3y...

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  3. Prove that the function f(x) = x+1/x(x!=0) is decreasing for all x in ...

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  4. Determine the area bounded by rectangular hyperbola xy=c^2 the x-axis ...

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  5. The direction agnles of a straight line are 120^@,45^@,30^@. Is the s...

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  6. Find K, for which the two planes x+ky+5z+2=0 and 3x-2y+kz-1=0 are perp...

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  7. Prove that, if P(A//B)=P(A) then P(A^c//B)=P(A^c).

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  8. Find the probability of guessing correctly at least 5 of the eight ans...

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  9. Solve: tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)= tan^(-1)3x.

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  10. If A=[[1,2,5].[-1,3,-4]] and B= [[3,-2,1],[0,-1,4],[5,2,-1]] show that...

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  11. If A= [[3,-1],[1,2]],B=[[3],[1]],C=[[1],[-2]] find the matrix X such t...

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  12. Prove that [[a^2,bc,c^2+ca],[a^2+ab,b^2,ca],[ab,b^2+bc,c^2]]= 4a^2b^2c...

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  13. If x^2+y^2= t-1/t and x^4+y^4 = t^2+1/t^2,show that , x^3y (dy)/(dx) =...

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  14. If 2x= y^(1/5)+y^(-1/5) prove that (x^2-1)y2+xy1 = 25y

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  15. Solve: (2x+4y+3)(dy)/(dx)= 2y+x+1

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  16. Solve: x(1-x^2)dy+(2x^2y-y-5x^3)dx=0.

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  17. If the magnitude of difference of two unit vectors is sqrt3, then show...

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  18. If the vector ahat i+ a hat j+ c hatk, hat i+hatk and chat i+c hat j+b...

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  19. Evaluate : int(-pi/2)^(pi/2)[f(x)+f(-x)][g(x)+g(-x)] dx

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  20. Using the definition of difinite integral as the limit of sum , evalua...

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