Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are ∞ or −∞, and describe the corresponding vertical asymptote. limx→0±sin⁡x|x|

The given limit is limx→0±sin⁡x|x| Obtain the right hand limit as shown below: limx→0+sin⁡x|x|=limx→0+sin⁡xx =1 Obtain the left hand limit as shown below: limx→0−sin⁡x|x|=limx→0−sin⁡x−x =−1

Find out the answer to "Determine the one-sided limits numerically or graphically. If..."

High School
Calculus and Analysis
Calculus 1
Limits and continuity

Rivka Thorpe

Answered question

2021-11-06

Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are

\infty

- \infty

, and describe the corresponding vertical asymptote.

lim_{x \to 0^{\pm}} \frac{\sin x}{| x |}

Answer & Explanation

curwyrm

Skilled2021-11-07Added 87 answers

The given limit is

lim_{x \to 0^{\pm}} \frac{\sin x}{| x |}

Obtain the right hand limit as shown below:

lim_{x \to 0^{+}} \frac{\sin x}{| x |} = lim_{x \to 0^{+}} \frac{\sin x}{x}

= 1

Obtain the left hand limit as shown below:

lim_{x \to 0^{-}} \frac{\sin x}{| x |} = lim_{x \to 0^{-}} \frac{\sin x}{- x}

= - 1

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f (x, y) = x^{3} - 6 x y + 8 y^{3}$
$\frac{1}{\sec (x)}$ in derivative?
What is the derivative of $\ln (x + 1)$ ?
What is the limit of $e^{- x}$ as $x \to \infty$ ?
What is the derivative of $f (x) = 5^{\ln x}$ ?
What is the derivative of $e^{- 2 x}$ ?
How to find $lim \frac{e^{t} - 1}{t}$ as $t \to 0$ using l'Hospital's Rule?
What is the integral of $\sqrt{9 - x^{2}}$ ?
What is the derivative of $f (x) = \ln [x^{9} {(x + 3)}^{6} {(x^{2} + 7)}^{5}]$ ?
What Is the common difference or common ratio of the sequence 2, 5, 8, 11...?
How to find the derivative of $y = e^{5 x}$ ?
How to evaluate the limit $\frac{\sin (5 x)}{x}$ as x approaches 0?
How to find derivatives of parametric functions?
What is the antiderivative of $- 5 e^{x - 1}$ ?
How to evaluate: indefinite integral $\frac{1 + x}{1 + x^{2}} d x$ ?

Didn't find what you were looking for?