Number of solutions of the equation 2^x + x = | vedclass

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Question

$\because x \geq \sin x \forall x \in[0,10 \pi]$

$\Rightarrow x+2^{x} \geq \sin x+2^{\sin x} \forall x \in[0,10 \pi]$

and equality holds only at

Vedclass · Accepted Answer

$1$

Vedclass · Answer

$\because x \geq \sin x \forall x \in[0,10 \pi]$

$\Rightarrow x+2^{x} \geq \sin x+2^{\sin x} \forall x \in[0,10 \pi]$

and equality holds only at $x=0$

Number of solutions of the equation $2^x + x = 2^{sin \ x} + \sin x$ in $[0,10\pi ]$ is -

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