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Starting from underset(xrarra)"lim"(x^(n...

Starting from `underset(xrarra)"lim"(x^(n)-a^(n))/(x-a)=na^(n-1)" deduce that ," underset(xrarr0)"lim"((1+x)^(n)-1)/(x)=n.`

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Show : underset(xrarr2)"lim"((1+x)^(n)-3^(n))/(x-2)=n.3^(n-1)

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CHHAYA PUBLICATION-LIMIT-EXERCISE 2 (Very Short Answer Type Questions )
  1. Distinguish between underset(xrarra)"lim"f(x)andf(a)

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  2. Using underset(xrarr0)"lim"(e^(x)-1)/(x)=1" deduce that ," underset(xr...

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  3. Starting from underset(xrarra)"lim"(x^(n)-a^(n))/(x-a)=na^(n-1)" deduc...

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  4. Using underset(xrarra)"lim"(e^(x)-1)/(x)" ,show that ," underset(xrarr...

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  5. Prove each of the following limits by graphical methods : underset(x...

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  6. Prove each of the following limits by intuitive and graphical methods ...

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  7. Prove each of the following limits by intuitive and graphical methods ...

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  8. Prove each of the following limits by intuitive and graphical methods ...

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  9. Prove that : underset(xrarr3)"lim"(x^(2)-9)/(x-3)=6

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  10. If f(x)=sqrt(x-3), " does "underset(xrarr3)"lim"f(x) exist ? Give rea...

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  11. A function phi(x) is defined as follows : phi(x){:(= 2," when"xne1)...

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  12. If f(x)=(|x|)/(x),"show that ,"underset(xrarr0)"lim"f(x) does not ex...

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  13. Evaluate the following limits : underset(xrarr2)"lim"(x(x^(2)-4))/...

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  14. Evaluate the following limits : underset(hrarr1)"lim"(h^(2)+2h-3)/(...

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  15. Evaluate the following limits : underset(hrarr-(1)/(2))"lim"(6x^(2)...

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  16. Evaluate the following limits : underset(urarr-3)"lim"[(1)/(u+3)+(6...

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  17. Evaluate the following limits : underset(xrarr1)"lim"(x^(3)-1)/(x^(...

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  18. Evaluate the following limits : underset(xrarr1)"lim"(x^(2)+5x-6)/(...

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  19. Evaluate the following limits : underset(xrarr(a)/(2))"lim"(8x^(2)-...

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  20. Evaluate the following limits : underset(xrarr(1)/(2))"lim"(8x^(3)-...

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