limit as x approaches 3+of (x^2+1)/(x-3)

Lösung

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

\infty

Schritte zur Lösung

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

\frac{x ^{2} + 1}{x - 3} = (x^{2} + 1) \frac{1}{x - 3}

= x \to 3 + lim ((x^{2} + 1) \frac{1}{x - 3})

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 (x^{2} + 1) \cdot x \to 3 + lim (\frac{1}{x - 3})

x \to 3 + lim (x^{2} + 1) = 10

x \to 3 + lim (\frac{1}{x - 3}) = \infty

= 10 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

s l o p e (- 8, - 2), (1, 4)

\frac{\partial}{\partial x} (9 y cos (x y))

\frac{\partial}{\partial x} ((x^{2} + x - y)^{7})

\frac{d}{d x} (6 + cos (3 x))

x \to 0 + lim (\frac{3 ^{x} - 1}{x ^{2}})