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Show that f(x)={{:(|2x-3|[x]", "xge1),(s...

Show that `f(x)={{:(|2x-3|[x]", "xge1),(sin((pix)/2)", "xlt1):}` is continuous but not differentiable at x = 1.

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Knowledge Check

  • The function f(x) = {{:(|2x-3|[x], x ge 1),(sin(pix)/2, x lt 1):}

    A
    is continuous at x = 2
    B
    is differentiable at x = 1
    C
    is continuous but not differentiable at x = 1
    D
    none of these

  • The function f(x) ={{:(e^(2x)-1,","x lt 0),(ax+(bx^2)/2-,","xlt0):} continuous and differentiable for

    A
    `a=1,b=2`
    B
    `a=2,b=1`
    C
    `a=2`, any b
    D
    any `a,b=4`

  • The function f(x)={(e^(2x)-1, x lt0),(ax^2+(bx^2)/2-1, xge0):} continuous and differentiable for

    A
    a=1, b=2
    B
    a=2, b=1
    C
    a=2, any b
    D
    any a, b=4

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