What is the limit as x approaches pi of ((e^{sin(x)}-1))/(x-pi) ?

The limit as x approaches pi of ((e^{sin(x)}-1))/(x-pi) is -1

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limit as x approaches pi of ((e^{sin(x)}-1))/(x-pi)

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

- 1

Solution steps

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

Apply L'Hopital's Rule

: x \to π lim (\frac{e ^{s i n (x)} cos ( x )}{1})

= x \to π lim (\frac{e ^{s i n (x)} cos ( x )}{1})

Plug in the value

x = π

= \frac{e ^{s i n (π)} cos ( π )}{1}

Simplify

\frac{e ^{s i n (π)} cos ( π )}{1} : - 1

= - 1

x \to - \infty lim (7 x e^{x})

\frac{d y}{d x}, arctan (x y) = arcsin (2 x + 2 y), (0, 0)

2 t y^{^{'}} - 4 y = 4 t^{4} e^{t^{2}}

\frac{\partial}{\partial x} (4 e^{5 x y})

x \to + 0 lim (\frac{1}{csc ( x )})

What is the limit as x approaches pi of ((e^{sin(x)}-1))/(x-pi) ?
The limit as x approaches pi of ((e^{sin(x)}-1))/(x-pi) is -1