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f(x)=2x+3 if x<= 2 and f(x)=2x-3 if x > ...

`f(x)=2x+3` if `x<= 2` and `f(x)=2x-3` if `x > 2`

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`f(x)={{:(2x+3",", if x le 2),(2x - 3",", if x gt 2):}`
Let 2 + h = x
`rArr 2 + h to 2`
`rArr h to 2`
` f(x) = 2 xx2 + 3 = 7`
R.H.L. ` underset (x to 2^(+))(lim)f(x)`
` underset (h to 0)(lim)f(1 + h)`
` underset (h to 0)(lim)2(2 + h)-3`
2(2 + 0) -3 = 1
`:'` f(2) `ne ` R.H.L.
`:.` f(x) is discontinuous at x = 2
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NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5.1
  1. Prove that the function f(x)=x^nis continuous at x = n, where n is a ...

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  2. Is the function f defined by f(x)={{:(x, if x le 1),(5, if x gt 1):...

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  3. f(x)=2x+3 if x<= 2 and f(x)=2x-3 if x > 2

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  4. f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3)...

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  5. {{:((|x|)/(x)","if x ne 0 ),(0"," if x = 0 ):}

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  6. {{:((x)/(|x|)","if x lt 0 ),(-1"," if x ge 0 ):}

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  7. f(x) {{:(x + 1"," if x ge 1 ),(x^(2)+ 1"," if x lt 1):}

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  8. f(x){{:(x^(3) - 3"," if x le 2 ),(x^(2) + 1"," if x gt 2 ):}

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  9. f(x){{:(10^(3) - 1"," if x le 1 ),(x^(2) "," if x gt 1 ):}

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  10. Is the function defined by f(x)={x+5, ifxlt=1x-5, ifx >1 a continuous...

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  11. Discuss the continuity of the function f, where f is defined by f(x){{...

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  12. f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}

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  13. f(x) {{:(-2"," if x le -1),(2x"," if -1lt x le 1),(2"," if x gt 1):}

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  14. Find the relationship between a and b so that the function f defined ...

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  15. For what value of lambdais the function defined by f(x)={lambda(x^2-2...

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  16. Show that the function defined by g(x)=x-[x] is discontinuous at all i...

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  17. Is the function defined by f(x)=x^2-sinx+5continuous at x=pi?

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  18. Discuss the continuity of the following functions:(a) f(x) = s in x + ...

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  19. Discuss the continuity of the cosine, cosecant, secant and cotangen...

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  20. Find all points of discontinuity of f, wheref(x)={(sinx)/x , ifx<0x+1,...

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