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Prove : underset(xrarr0)"lim"(1-cosxsqrt...

Prove : `underset(xrarr0)"lim"(1-cosxsqrt(cos2x))/(x^(2))=(3)/(2)`

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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 ( Long Answer Type Questions)
  1. Prove : underset(xrarr4)"lim"(3-sqrt(5+x))/(1-sqrt(5-x))=-(1)/(3)

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  2. Prove : underset(xrarr1)"lim"(x^(2)-sqrt(x))/(sqrt(x)-1)=3

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  3. Prove : underset(xrarr0)"lim"(1-cosxsqrt(cos2x))/(x^(2))=(3)/(2)

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

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  5. Prove : underset(xrarroo)"lim"sqrt(x)[sqrt(x+2)-sqrt(x)]=1

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  6. Prove : underset(xrarroo)"lim"[sqrt(1+x+x^(2))-x]=(1)/(2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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