limit as x approaches-3+of-(sin(c-3x))/(e^{5x+15)-1}

Lösung

x \to - 3 + lim (- \frac{sin ( c - 3 x )}{e ^{5 x + 15} - 1})

\infty

Schritte zur Lösung

x \to - 3 + lim (- \frac{sin ( c - 3 x )}{e ^{5 x + 15} - 1})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - x \to - 3 + lim (\frac{sin ( c - 3 x )}{e ^{5 x + 15} - 1})

\frac{sin ( c - 3 x )}{e ^{5 x + 15} - 1} = sin (c - 3 x) \frac{1}{e ^{5 x + 15} - 1}

= - x \to - 3 + lim (sin (c - 3 x) \frac{1}{e ^{5 x + 15} - 1})

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

= - x \to - 3 + lim (sin (c - 3 x)) \cdot x \to - 3 + lim (\frac{1}{e ^{5 x + 15} - 1})

x \to - 3 + lim (sin (c - 3 x)) = sin (c + 9)

x \to - 3 + lim (\frac{1}{e ^{5 x + 15} - 1}) = \infty

= - sin (c + 9) \cdot \infty

Vereinfache

- sin (c + 9) \cdot \infty : \infty

= \infty

x \to 0 + lim (\frac{e ^{x} - 1 - x}{x ^{2}})

t \to \infty lim (t e^{t})

x \to 0 lim (\frac{3}{2})

x \to 0 + lim (x^{9} (ln (x))^{2})

x \to π lim (- cos (x))