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Find the values of the following limts :...

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

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The correct Answer is:
`(1)/(2)`
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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Long Answer Type Questions)
  1. Find the values of the following limts : underset(nrarroo)"lim"(1^(2...

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

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

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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 follwing limts : underset(nrarroo)"lim"(1.2+2...

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Putting x=theta-(pi)/(4)" prove that "underset(thetararr(pi)/(4))"lim"...

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  19. A function f (x) is defined as follwos : f(x){:(=1,","" when " xne0...

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  20. Prove : underset(xrarr1)"lim"(4^(x)-4)/(x-1)=8log(e)2

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