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Find the values of the following limts :...

Find the values of the following limts :
`underset(nrarroo)"lim"(1+2+3+...+n)/(n^(2))`

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The correct Answer is:
`(1)/(2)`
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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Long Answer Type Questions)
  1. Prove : underset(xrarroo)"lim"[sqrt(1+x+x^(2))-x]=(1)/(2)

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  2. Prove : underset(nrarroo)"lim"[root(3)(n+1)-root(3)(n)]=0

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  3. Find the values of the following limts : underset(nrarroo)"lim"(1+2+...

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  4. Find the values of the following limts : underset(nrarroo)"lim"(1^(2...

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  5. Find the values of the following limts : underset(nrarroo)"lim"(1+(1...

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  6. Find the values of the following limts : underset(nrarroo)"lim"((1)/...

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  7. Find the values of the following limts : underset(nrarroo)"lim"(1+2+...

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  8. Find the values of the follwing limts : underset(nrarroo)"lim"(1.2+2...

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  9. prove the underset(nrarroo)"lim"(a.e^(x)+b.e^(-x))/(c.e^(x)+d.e^(-x))=...

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  10. Show that underset(nrarroo)"lim"(a.e^(x)+b.e^(-x))/(c.e^(x)+d.e^(-x))=...

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  11. Do the following limits exist ? underset(xrarrpi)"lim"(1)/(pi-x)

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  12. Do the following limits exist ? underset(xrarr0)"lim""Xcos"(1)/(x)

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  13. Does underset(xrarr4)"lim"sqrt(4-x) exist ?

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  14. Does underset(xrarr4)"lim"sqrt(4-x) exist ?

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  15. Prove : underset(xrarr0)"lim""xcos"(1)/(x)=0

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  16. Prove : underset(xrarr0)"lim"x^(2)"sin"(1)/(x)=0

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  17. Prove : underset(xrarr0)"lim"(x^(2)sin^(1/x))=0

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  18. Prove : underset(xrarroo)"lim"(sinx)/(x)=0

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  19. Prove : underset(xrarroo)"lim"(cosx)/(x)=0

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  20. Putting z=x-(pi)/(4)" show that "underset(xrarr(pi)/(4))"lim"(1-tanx)/...

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