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

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

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limit as x approaches 1-of (-3x-1)/(x-1)

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

\infty

Solution steps

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

Multiply by the conjugate of

x - 1 : \frac{x ^{2} - 1}{x + 1}

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

Divide by highest denominator power:

- \frac{3 x}{x - 1} - \frac{1}{x - 1}

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

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

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

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

= - (- \infty) - (- \infty)

Apply Infinity Property:

\infty + \infty = \infty

= \infty

x \to \frac{π}{2} lim (x - \frac{π}{2})

\frac{\partial}{\partial z} (x^{2} + yz)

f (x) = x^{2} + 2 x, at x = 1

\int \frac{1}{b y ^{2} + b ^{3}} d y

\int \frac{1}{x 9 x ^{2} + 64} d x

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