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For what value of k is the following f...

For what value of `k` is the following function continuous at `x=2?` `f(x)={2x+1; x<2 k ; x=2 3x-1; x >2}`

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To determine the value of \( k \) that makes the function \( f(x) \) continuous at \( x = 2 \), we need to ensure that the following condition holds: \[ \lim_{x \to 2^-} f(x) = f(2) = \lim_{x \to 2^+} f(x) \] Given the function: ...
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Knowledge Check

  • If f(x)={{:((sqrt(1-cos2x))/(sqrt(2)x)",",xne0),(k",",x=0):} then which value of k will make function f continuous at x=0 ?

    A
    1
    B
    `-1`
    C
    0
    D
    no value

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