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Evaluate the following limits: lim(x to ...

Evaluate the following limits: `lim_(x to 0)[(1)/(x)-log(1+x)/(x^(2))]`

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CHHAYA PUBLICATION-LIMIT-EXAMPLE
  1. If lim(x to 0)(1+x)^(1/x)=e, prove that lim(x to 0)(1+3x)^(((x+2))/(x)...

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  2. Evaluate the following limits: lim(x to 3)sin(e^(x-3)-1)/(log(x-2))

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  3. Evaluate the following limits: lim(x to 0)[(1)/(x)-log(1+x)/(x^(2))]

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  4. Evaluate the following limits: lim(x rarr 0)(xe^(x)-log(1+x))/(x^(2))

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  5. Find the value of : lim(x rarr oo) ((x+5)/(x+1))^(5)

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  6. Find the value of : lim(x rarr oo) ((x+5)/(x-1))^(5)

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

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  8. Does underset(xrarr2)"lim"(x^(2)-4)/(x-2) exist If so , find its val...

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

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  10. Draw the graph of y=f(x)=(x^(2))/(x) and from the graph examine wheth...

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  11. Draw the graph of the function f(x)=(|x|)/(x) and from the graph disc...

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  12. Let f(x){:(=x^(2),","" when "xlt1),(=1,",""when "xle1):} Draw t...

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  13. Show that underset(xrarr1)"lim"(1)/(x-1)^(2)=+oo .

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  14. Evaluate : underset(xrarr0)"lim"(1)/(x) .

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  15. Evaluate : underset(xrarr-oo)"lim"(1+(2)/(x^(2))).

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  16. Prove that underset(xrarroo)"lim"(1)/(x)=0.

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  17. Show that underset(xrarr2)"lim"(x^(2)-3x+5)=3.

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  18. Prove that underset(xrarr2)"lim"(x^(2)-3x+5)=3. Where n is a positive ...

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  19. Evaluate : underset(yrarr-1)"lim "(y^(2)-3y+6)/(2y^(2)+5y) .

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  20. If p(x)=a(0)x^(n)+a(1)x^(n-1)+a(2)x^(n-2)+.....+a(n-1)x+a(n)," prove t...

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