Find out the answer to "Calculating limits. Determine the following limits. limx→−∞(|x−1|+x) and..."

facas9

Answered question

2021-11-09

Calculating limits. Determine the following limits.

lim_{x \to - \infty} (| x - 1 | + x)

and

lim_{x \to \infty} (| x - 1 | + x)

Demi-Leigh Barrera

Skilled2021-11-10Added 97 answers

Given

lim_{x \to - \infty} (| x - 1 | + x)

and

lim_{x \to \infty} (| x - 1 | + x)

Now the limit

lim_{x \to - \infty} (| x - 1 | + x)

Here

| x - 1 | = - (x - 1)

when

x \to - \infty

Now

lim_{x \to - \infty} (| x - 1 | + x) = lim_{x \to - \infty} (- (x - 1) + x)

= lim_{x \to - \infty} (- x + 1 + x)

= lim_{x \to - \infty} (1)

= 1

And the limit

lim_{x \to \infty} (| x - 1 | + x)

Here

| x - 1 | = (x - 1)

when

x \to \infty

Now

lim_{x \to \infty} (| x - 1 | + x) = lim_{x \to \infty} ((x - 1) + x)

= lim_{x \to \infty} (x - 1 + x)

= lim_{x \to \infty} (2 x - 1)

= (2 (\infty) - 1)

= \infty

Final answer:

lim_{x \to - \infty} (| x - 1 | + x) = 1

and

lim_{x \to - \infty} (| x - 1 | + x) = \infty

Jeffrey Jordon

Expert2022-06-26Added 2605 answers

Answer is given below (on video)

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