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A function f (x) is defined as follwos :...

A function f (x) is defined as follwos :
f(x)`{:(=1,","" when " xne0),(=0,","" when " x=0):}`
Does `underset(xrarr0)"lim"f(x)` exist ?

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CHHAYA PUBLICATION-LIMIT-EXAMPLE
  1. Find the value of : lim(x rarr oo) ((x+5)/(x-1))^(5)

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. 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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  16. Evaluate : underset(xrarr1)"lim"sin(2x^(2)-x-1).

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  17. show that underset(xrarr-2)"lim"sqrt(x^(3)+3x^(2)-x+3)=3

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  18. Evaluate : underset(hrarr0)"lim"e^(2)h^(2-3h+2)

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  19. Prove that underset(xrarr4)"lim"log(2.x^(3//2)-3.x^(1//2)-1)=2log3.

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  20. Show that underset(thetararralpha)"lim"sintheta=sinalpha.

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