If f(x) = kx - sin x is monotonically increas | vedclass

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(A) function $f(x)$ is monotonically increasing if $f'(x) \geq 0$ for all $x \in R$.Given $f(x) = kx - \sin x$.Differentiating with respect to $x$,we

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$k > 1$

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(A) function $f(x)$ is monotonically increasing if $f'(x) \geq 0$ for all $x \in R$.Given $f(x) = kx - \sin x$.Differentiating with respect to $x$,we get $f'(x) = k - \cos x$.For $f(x)$ to be monotonically increasing,$f'(x) \geq 0$ for all $x \in R$.$k - \cos x \geq 0 \implies k \geq \cos x$.Since the maximum value of $\cos x$ is $1$,for $k \geq \cos x$ to hold for all $x$,$k$ must be greater than or equal to the maximum value of $\cos x$.Therefore,$k \geq 1$.

If $f(x) = kx - \sin x$ is monotonically increasing,then

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