Question

# Find the value of k, if the function f is given by f(x)=⎧⎪ ⎪⎨⎪ ⎪⎩√3−tanxπ−3x,x≠π3k,x=π3 is continuous at x=π3.

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Solution

## Given the function f(x) is continuous at x=π3.Then limx→π3√3−tanxπ−3x=f(π3)Now using L'Hospital's rule we get,or, limx→π3−sec2x−3=f(π3)or, 43=f(π3)or, k=43.

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