What is the limit as x approaches 0 of (e^x-2)/(sin(7x)) ?

The limit as x approaches 0 of (e^x-2)/(sin(7x)) is diverges

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limit as x approaches 0 of (e^x-2)/(sin(7x))

x \to 0 lim (\frac{e ^{x} - 2}{sin ( 7 x )})

diverges

Solution steps

x \to 0 lim (\frac{e ^{x} - 2}{sin ( 7 x )})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim (\frac{e ^{x} - 2}{sin ( 7 x )}) = - \infty

x \to 0 - lim (\frac{e ^{x} - 2}{sin ( 7 x )}) = \infty

= diverges

x \to - 6 + lim ((x + 6) ln ((x + 6)^{2}))

t \to 1 lim (\frac{t ^{2} - 0}{t - 0})

x \to 0 lim (tan^{x^{2}} (x))

x \to 0 lim (\frac{\frac{5}{6 + x} - \frac{5}{6}}{x})

x \to 5 lim (\frac{1}{2} (x + 3))

What is the limit as x approaches 0 of (e^x-2)/(sin(7x)) ?
The limit as x approaches 0 of (e^x-2)/(sin(7x)) is diverges