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Calculate lim(x to 2) , where f(x) = {{:...

Calculate `lim_(x to 2) `, where `f(x) = {{:(3 if ,x le 2),(4 if, x gt 2):}`

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The correct Answer is:
`underset(x to 2)(lim) f(x)` does not exist
`underset(x to 2)(lim) f(x) != underset(x to 2^(+))(lim) f(x)`
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Find 'k' so that : lim_(x to 2) f(x) exists, where : f(x)={{:(2x+3",", "if "x le 2), (x+k",", "if "x gt 2):}

If f(x)={:{(x+2", if " x le 4),(x+4", if " x gt 4):} , then

f(x)={{:(3x-8, if x le 5),(2k, if x gt 5) :} at x = 5

f(x)={{:(3x-8, if x le 5),(2k, if x gt 5) :} at x = 5

Find 'k' so that : lim_(x to 2) f(x) exists, where : f(x)={{:(2x+3",", "if "x le 2), (x+3k",", "if "x gt 2):}

Find 'k' so that : lim_(x to 2) f(x) exists, where : f(x)={{:(2x+3",", "if "x le 2), (x+2k",", "if "x gt 2):}

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Knowledge Check

  • Find 'k' so that : lim_(x to 2) f(x) exists, where : f(x)={{:(2x+3",", "if "x le 2), (x+k",", "if "x gt 2):}

    A
    3
    B
    4
    C
    5
    D
    6

  • If f(x)={:{(x+2", if " x le 4),(x+4", if " x gt 4):} , then

    A
    `underset( x rarr 4^(+))lim f(x)=6`
    B
    `underset(x rarr 4^(-))lim f(x)=8`
    C
    f has removable discontinuity
    D
    f has irremovable discontinuity

  • Find 'k' so that : lim_(x to 2) f(x) exists, where : f(x)={{:(2x+3",", "if "x le 2), (x+2k",", "if "x gt 2):}

    A
    `5/2`
    B
    `5`
    C
    `2`
    D
    `1/2`