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Verify the existence of lim(x to 3) f(x)...

Verify the existence of `lim_(x to 3) f(x)`, where `f(x)={:{(|x-3|/(x-3),for , xne 3),(0, for ,x =3):}`

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does not exist
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FULL MARKS-DIFFERENTIAL CALCULUS - LIMITS AND CONTINUITY-EXERCISE 9.1
  1. Complete the table use the result the estimate the limits lim( x to ...

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  2. Find the value of limit lim(x to 0) (x (e^(x) -1))/(1-cosx)

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  3. Find the limits lim(x to 4) (x^3 - 64)/(x^2 -16)

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  4. Find the limits lim(x to 1) (x^2+2)

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  5. Find the limits lim(x to 2) f(x) where f(x)={:{(4-x,x ne2),(0,x=2):}

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  6. Find the limits lim (x to 1) f(x) where f(x)={:{(x^2+2,x ne1),(1,x=1...

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  7. Find the limits lim( x to 3) 1/(x-3)

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  8. Find the limits lim(x to 5) (-|x-5|)/((x-5))

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  9. Find the limits lim(x to 1) (pi x)

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  10. Find the limits lim(x to 0) (sec x)

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  11. Find the limits lim(x to pi/2) tan x

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  12. Sketch graph and identify the values of x for which lim f(x) exists. ...

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  13. Find the point of discontinuity of the function f(x)={:{(sinx,x lt 0...

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  14. Sketch the graph of a function f that satifies the given values: f(0...

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  15. Sketch the graph of a function f that satifies the given values: f(-...

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  16. Write a brief description of the meaning of the notation lim(x to 8) f...

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  17. If f(2)=4, can you conclude anything about the limit of f(x) as x appr...

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  18. If the limit of f(x) as x approaches 2 is 4, can you conclude anything...

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  19. Evaluate : lim(x to 2) (x^2-4)/(x-2) if it exists by finding f(2^-) an...

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  20. Verify the existence of lim(x to 3) f(x), where f(x)={:{(|x-3|/(x-3),f...

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