What is the limit as x approaches 0 of e^{xsin(1/x)} ?

The limit as x approaches 0 of e^{xsin(1/x)} is 1

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limit as x approaches 0 of e^{xsin(1/x)}

x \to 0 lim (e^{x s i n (\frac{1}{x})})

1

Solution steps

x \to 0 lim (e^{x s i n (\frac{1}{x})})

Apply the Squeeze Theorem:

1

= 1

y = 3

\int \frac{1}{1 - y ^{2}} d y

f (x) = x^{4 x}

e^{- 3 x} + e^{2 x}

\int \frac{8 - 128 x}{49 - 64 x ^{2}} d x

What is the limit as x approaches 0 of e^{xsin(1/x)} ?
The limit as x approaches 0 of e^{xsin(1/x)} is 1