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Prove that underset(x rarr 0)lim (log(1+...

Prove that `underset(x rarr 0)lim (log(1+x)+sinx)/(e^x-1) =2`

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UNITED BOOK HOUSE-SET 7-EXERCISE
  1. Show that |[cos 15^@ sin 15^@],[sin 75^@ cos 75^@]| =0

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  2. If A = ([3,5],[2,a]),B=([4,b],[2,9]) and C = ([26,a],[14,45]) find a a...

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  3. Prove that underset(x rarr 0)lim (log(1+x)+sinx)/(e^x-1) =2

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  4. If y = log{sinsqrt(x^2+1)} find (dy)/(dx)

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  5. Evaluate: int(e^(x loga)+e^(a log x)) dx

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  6. Write the order and degree of the differential equation ((d^2y)/(dx^2)...

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  7. Divide 24 into two parts such that their product is maximum.

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  8. If f(x) = 3x^2+15x+5, then find the approximate value of f(3.02), usin...

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  9. Can the numbers 1/2,-1/sqrt2, -1/2 be the direction cosines of a strai...

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  10. Find the equation of the line passing through the point(1,2,3) and par...

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  11. Two unbiased dice are thrown. Find the probability that the sum of the...

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  12. M and E are two equally strong football teams. Findthe probability tha...

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  13. Solve: tan^(-1)sqrt(x(x+1)+sin^(-1)sqrt(1+x+x^2) = pi/2

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  14. If A = [[1,-1],[2,-1]],B = [[a,1],[b,-1]] and (A+B)^2 = A^2+B^2 find a...

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  15. Evaluate: |[alpha, beta,gamma],[alpha^2,beta^2,gamma^2],[beta+gamma,ga...

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  16. Show that |[-1,b,c],[a,-1,c],[a,b,-1]|=(a+1)(b+1)(c+1)(a/(a+1)+b/(b+1...

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  17. If y = tan^(-1) ((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) ...

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  18. Evaluate: int (cos x-sinx )/sqrt(sin 2x)dx

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  19. Evaluate: int x sqrt((a^2-x^2)/(a^2+x^2))dx

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  20. Solve: cos^(-1)((dy)/(dx)) = x+y.

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