What is the limit as x approaches 1+of ln(x-1)+3x ?

The limit as x approaches 1+of ln(x-1)+3x is -infinity

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limit as x approaches 1+of ln(x-1)+3x

x \to 1 + lim (ln (x - 1) + 3 x)

- \infty

Solution steps

x \to 1 + lim (ln (x - 1) + 3 x)

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

With the exception of indeterminate form

= x \to 1 + lim (ln (x - 1)) + x \to 1 + lim (3 x)

x \to 1 + lim (ln (x - 1)) = - \infty

x \to 1 + lim (3 x) = 3

= - \infty + 3

Apply Infinity Property:

- \infty + c = - \infty

= - \infty

x \to 0 lim (4 x^{2} + 5 x - 6)

x \to 7 lim (\frac{8 x}{x - 7})

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

x \to 3 - lim (∣ x + 1 ∣ + 2)

x \to \frac{π}{2} + lim (x tan (x))

What is the limit as x approaches 1+of ln(x-1)+3x ?
The limit as x approaches 1+of ln(x-1)+3x is -infinity