In the graph of the function sqrt{3} sin x + | vedclass

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(B) The function is given by $f(x) = \sqrt{3} \sin x + \cos x$.To find the maximum distance from the $x$-axis,we need to find the maximum absolute val

Vedclass · Accepted Answer

$2$

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(B) The function is given by $f(x) = \sqrt{3} \sin x + \cos x$.To find the maximum distance from the $x$-axis,we need to find the maximum absolute value of the function,which is $|f(x)|_{max}$.For a function of the form $f(x) = a \sin x + b \cos x$,the maximum value is $\sqrt{a^2 + b^2}$ and the minimum value is $-\sqrt{a^2 + b^2}$.Here,$a = \sqrt{3}$ and $b = 1$.Maximum value $= \sqrt{(\sqrt{3})^2 + (1)^2} = \sqrt{3 + 1} = \sqrt{4} = 2$.Minimum value $= -\sqrt{(\sqrt{3})^2 + (1)^2} = -2$.The maximum distance from the $x$-axis is the maximum value of $|f(x)|$,which is $|2| = 2$ or $|-2| = 2$.Therefore,the maximum distance is $2$.

In the graph of the function $\sqrt{3} \sin x + \cos x$,the maximum distance of a point from the $x$-axis is:

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