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If f(x)=x|x|,prove that f'(x)=2|x|....

If f(x)=x|x|,prove that f'(x)=2|x|.

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UNITED BOOK HOUSE-TECHNO INDIA GROUP ACADEMIA,SOUTH KOLKATA.-EXERCISE
  1. Find the ratio in which the line segment joining A(2,4,5) and B(3,5,4)...

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  2. Evaluate :lim(hrarr0)(e^h h)/h-1

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  3. If f(x)=x|x|,prove that f'(x)=2|x|.

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  4. In a lottery there are 10 prizes and 25 blanks.Find the probability of...

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  5. Find mean and variance for the following data 5,9,8,12,6,10,6,8.

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  6. For any three sets A, B, C. show thatAxx(B-C)=(AxxB)-(AxxC)

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  7. In any /\ABC,prove that sin(B-C)/(sin(B+C))=(b^2-c^2)/(a^2)

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  8. Prove that,cosx/(1-sinx)=tan(pi/4+x/2)

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  9. Prove by mathematical induction that1/1.3+1/3.5+1/5.7+...+1/((2n-1)(2n...

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  10. If x+iy=2/(3+costheta+isintheta),show that 2x^2+2y^2=3x-1

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  11. find the co-efficient of (2r+4)th and (r-2)th terms in the expansion o...

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  12. If p, q, r are in G.P and the equation px^2+2qx+r=0 and dx^2+2ex+f=0 h...

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  13. Show that the points (a,0),(0,b)and (3a,-2b)are collinear.Also find th...

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  14. Find the distance between the parallel lines 4x-3y+5=0 and 4x-3y+7=0.

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  15. Find the equation of a circle through origin which cuts of intercepts ...

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  16. Find the value of the limit lim(nrarroo)(1^2+2^2+...+n^2)/n^3

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  17. If y=sqrt((1-x)/(1+x)),prove that (1-x^2)dy/dx+y=0

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  18. If x^2is an odd number then x is also odd number,justify the validity ...

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  19. If x and y are odd integers, then xy is also an odd integer r examine ...

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  20. In single throw of two dice,the probality of obtaning 'a total of 8' i...

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