What is the limit as x approaches 0+of cos(x)ln(x) ?

The limit as x approaches 0+of cos(x)ln(x) is -infinity

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limit as x approaches 0+of cos(x)ln(x)

x \to 0 + lim (cos (x) ln (x))

- \infty

Solution steps

x \to 0 + lim (cos (x) ln (x))

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

With the exception of indeterminate form

= x \to 0 + lim (cos (x)) \cdot x \to 0 + lim (ln (x))

x \to 0 + lim (cos (x)) = 1

x \to 0 + lim (ln (x)) = - \infty

= 1 \cdot (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

x \to 0 lim (\frac{sin ( x ) - x}{x sin ( x )})

\frac{\partial}{\partial y} (e^{x^{2} + y^{2}} \cdot 2 x)

\frac{d}{d x} (2 x^{3} ln (x))

\int (4 x^{3} - 9 x^{2} + 7 x + 3) e^{- x} d x

\frac{d}{d x} (e^{- x} + x - 1)

What is the limit as x approaches 0+of cos(x)ln(x) ?
The limit as x approaches 0+of cos(x)ln(x) is -infinity