What is the limit as x approaches 6-of ln(1/((6-x))) ?

The limit as x approaches 6-of ln(1/((6-x))) is infinity

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limit as x approaches 6-of ln(1/((6-x)))

x \to 6 - lim (ln (\frac{1}{( 6 - x )}))

\infty

Solution steps

x \to 6 - lim (ln (\frac{1}{6 - x}))

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= x \to 6 - lim (- ln (6 - x))

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

= - x \to 6 - lim (ln (6 - x))

Apply the Limit Chain Rule:

- \infty

= - (- \infty)

Simplify

= \infty

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

x \to 1 lim (\frac{ln ( x )}{x + 1})

x \to π lim (\frac{- 2}{π - x})

x \to - 6 lim (- x + 2)

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

What is the limit as x approaches 6-of ln(1/((6-x))) ?
The limit as x approaches 6-of ln(1/((6-x))) is infinity