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Evaluate: underset(nrarralpha)Lt[1/(sqrt...

Evaluate: `underset(nrarralpha)Lt[1/(sqrt(2n-1^2)) +1/(sqrt(4n-2^2))+1/sqrt(6n-3^2)+...+1/n]`

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Evaluate : underset(nrarrinfty)Lt[(1)/(sqrt(n^2 - 1^2)) + 1/(sqrt(n^2-2^2)) +1/(sqrt(n^2 - 3^2))+....+ 1/(sqrt(n^2 - (n-1)^2))]

Evaluate: ("lim")_(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt(3n^2)))

Evaluate : underset(nrarroo)"lim"(1+sqrt(n))/(1-sqrt(n))

Evaluate : underset(nrarroo)"lim"(sqrt(1+n^(2))-sqrt(1+n))/(sqrt(1+n^(3))-sqrt(1+n))

Find the value of underset(ntooo)lim[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt(n^(2)-3^(2)))+...+(1)/(sqrt(n^(2)-(n-1)^(2)))]

Find the value of lim_(nrarroo)[(1)/(sqrt(2n-1)^(2))+(1)/(sqrt(4n-2^(2)))+...+(1)/(n)] .

Prove that underset( n rarr infty) lim[1/n+sqrt(n^2-1^2)/n^2+sqrt(n^2-2^2)/n^2+…..sqrt(n^2-(n-1)^2)/n^2] = pi/4

Evaluate : underset (nrarrinfty)lim underset(r=0)overset(n-1)sum 1/sqrt(4n^2-r^2)

lim_(nrarroo) [(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]

Prove : underset(nrarroo)"lim"(sqrt(n+1)-sqrt(n))=0

UNITED BOOK HOUSE-SET 19-EXERCISE
  1. If x>1/2, show that the function f(x) = x(4x^2 - 3) is steadily increa...

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  2. If |veca| = sqrt3,|vecb| = 2 and veca.vecb = sqrt6, then find the angl...

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  3. If the line (x-2)/(6) = (y-1)/(lambda) = (z+5)/(-4) is perpendicular t...

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  4. The probability that A hits a target is 1/3 and the probability that B...

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  5. An unbiased coin is toosed 7 times. Find the probability of getting an...

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  6. answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...

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  7. Solve : |(x+4, 2x,2x),(2x , x+4, 2x),(2x, 2x, x+4)| = 0

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  8. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

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  9. If y^(1/3) + y^(-1/3) = 2x, prove that (x^2 - 1)y2 + xy1 = 9y.

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  10. Evaluate : int(loge(x+1))/((x+1)^2) dx

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  11. Evaluate :int(5^(5^(5^x)cdot 5^(5^(x))cdot 5^x))dx

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  12. Solve the differential equation: (1+y^2)+(x - e^(tan^-1 y) )dy/dx = 0

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  13. Find the unit vector which is perpendicular to both veca = 2hati + 3ha...

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  14. If veca = hati + hatj + hatk , vecb = hatj - hatk then find a vector v...

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  15. Evaluate: underset(nrarralpha)Lt[1/(sqrt(2n-1^2)) +1/(sqrt(4n-2^2))+1/...

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  16. Evaluate : int(0)^(pi/4) (sin^2xcos^2xdx)/((sin^3x+cos^3x)^2)

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  17. A discreate random variable x has the following probability distributi...

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  18. answer any two questions :(iii) if the straight line lx+my=n be a norm...

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  19. Find the area enclosed by the curves x^2=y , y=x+2 and x-axis

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  20. A 5 ft long man walks away from the foot of a 12 1/2 ft high lamp post...

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