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

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(D) Consider the function $f(t) = 2^t + t$. Since $f'(t) = 2^t \ln 2 + 1 > 0$ for all $t$,$f(t)$ is a strictly increasing function. The given equation

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$1$

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(D) Consider the function $f(t) = 2^t + t$. Since $f'(t) = 2^t \ln 2 + 1 > 0$ for all $t$,$f(t)$ is a strictly increasing function. The given equation is $f(x) = f(\sin x)$. Since $f$ is strictly increasing,$f(x) = f(\sin x)$ implies $x = \sin x$. In the interval $[0, 10\pi]$,the equation $x = \sin x$ holds only when $x = 0$. Thus,there is only $1$ solution in the given interval.

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

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