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sum(n=0)^oo1/(n !)[sum(k=0)^n(k+1)int0^1...

`sum_(n=0)^oo1/(n !)[sum_(k=0)^n(k+1)int_0^1 2^(-(k+1)x)dx]`

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A DAS GUPTA-Miscellaneous Exercises-Exercise
  1. Solve: (x^2 + 4y^2 + 4xy) dy = (x + 2y + 1) dx.

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  2. If the normal to the ellipse (x^(2))/9+(y^(2))/4=1 which is farthest f...

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  3. sum(n=0)^oo1/(n !)[sum(k=0)^n(k+1)int0^1 2^(-(k+1)x)dx]

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  4. Consider the family of circles x^2 + y^2= r^2 2 lt r lt 5. If in the f...

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  5. Let T1, T2 and be two tangents drawn from (-2, 0) onto the circle C:x^...

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  6. The equation of two equal sides AB and AC of an isosceies triangle ABC...

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  7. Find the equation of the largest circle with centre (1, 0) that can be...

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  8. Prove that the circle x^2 + y^2 -6y + 4 = 0 and the parabola y^(2) = x...

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  9. Find the equation of the ellipse whose foci are the points (1, 2) and ...

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  10. Let ABC and PQR be any two triangles in the same plane. Assume that th...

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  11. An unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6, is thrown n ti...

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  12. Find the smallest positive values of xa n dy satisfying x-y=pi/4a n dc...

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  13. log(3/4)log8(x^2+7)+log(1/2)log(1/4)(x^2+7)^(-1)=-2.

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  14. Total number of solutions of the equation x² -4-[x]=0 are (where (.) d...

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  15. Let a, b be the roots of the equation x^2 - kx + k = 0, k in R. If a^2...

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  16. Two parabola have the focus (3, 2). Their directrices are the x-axis a...

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  17. Let alpha in R. prove that a function f: R-R is differentiable at...

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  18. Find the lim(x to 0) frac{sqrt(x+2) -sqrt2}{root(3)(1-x) - sqrt(1+x)}.

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  19. Two parabolas y(2) = 4a(x – 1l(1)) and x(2) = 4a(y – l(2)) always touc...

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  20. Let 2x^2 +y^2-3xy = 0 be the equation of a pair of tangents drawn from...

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