Limits and Continuity Explained: Expert Help

Recent questions in Limits and continuity

Joni Kenny 2021-10-12

Determine the limit of each function analytically. Show neat and complete solution. (hint: some of the items need to be factored or rationalized for the limits to exist)
$lim_{x \to 2} \frac{{(3 x - 2)}^{2} - {(x + 2)}^{2}}{(x - 2)}$

Maiclubk 2021-10-12

Find the limits (that is, end behaviors) below.
$lim_{x \to - \infty} \frac{- 5 x (x - 9) (x + 6)}{6 - 8 x^{3}}$

ankarskogC 2021-10-12

Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers.
$lim_{x \to 0} \frac{x}{\sqrt{c x + 1} - 1}, c \neq 0$

rocedwrp 2021-10-12

Evaluate the following limits algebraically. If neccessary, select the most informative answer from infinity, negative infinity, and DNE (Does Not Exist)
$lim_{x \to 0} \frac{3}{x^{2}}$

vazelinahS 2021-10-12

Find the limits
$lim_{x \to \infty} \sqrt{\frac{8 x^{2} - 3}{2 x^{2} + x}}$

avissidep 2021-10-12

Use the LHospitals

Carol Gates 2021-10-11

Solve the following limit.
$lim_{x \to \infty} (\frac{3 x^{3} - 4 x + 2}{7 x^{3} + 5})$

Kyran Hudson 2021-10-11

Show that the limit leads to an indeterminate form. Then carry out the two-step procedure: Transform the function algebraically and evaluate using continuity.
$lim_{x \to 9} \frac{2 t - 18}{5 t - 45}$

usagirl007A 2021-09-11

Please, find the $lim i t lim_{x \to - 1} (\frac{{(x + 1)}^{2} (x - 1)}{x^{3} + 1})$

slaggingV 2021-08-19

Prove using the definition on the limit that
$lim_{n \to \infty} \frac{1 + n}{1 - 2 n} = \frac{- 1}{2}$

he298c 2021-06-07

Which of the following is NOT a result of the Central Limit Theorem? Choose the correct answer below.
a) As the sample size increases, the distribution of the sample means x-bar will approach a normal distribution.
b) The distribution of the sample data will approach a normal distribution as the sample size increases.
c) The variance of all sample means is the population variance divided by the square root of the sample size.
d) The mean of all sample means is the population mean $μ$

ruigE 2021-05-27

Evaluate $lim_{x \to \infty} \frac{\sin h x}{e^{x}}$

fortdefruitI 2021-05-22

Analysis of the voltage in a hairdryer involves terms of the form $\sin (n w t - 90^{\circ})$ , where n is a positive integer, w is the frequency of the voltage, and t is time. Use an identity to simplify this expression.

Emily-Jane Bray 2021-05-16

Find the limit (if it exists) and discuss the continuity of the function. $lim_{(x, y) \to (0, 0)} \frac{y + x e^{- y ²}}{1 + x ²}$

ankarskogC 2021-05-02

Find the limit, if it exists. (If an answer does not exist, enter DNE.)
$lim \arctan (e^{x})$
$x \approx \infty$

sodni3 2021-05-01

Find the limit and discuss the continuity of the function. $lim_{x, y} \to (0, 1) \frac{\arccos (\frac{x}{y})}{1} + x y$

sanuluy 2021-03-11

Evaluate the following limits.
$lim_{(x, y) \to (4, 5)} \frac{\sqrt{x + y} - 3}{x + y - 9}$

UkusakazaL 2021-03-09

Find the limits:
$lim_{x \to - 2} \frac{x + 2}{\sqrt{x^{2} + 5} - 3}$

Elleanor Mckenzie 2021-03-09

Find each of the following limits. If the limit is not finite, indicate or for one- or two-sided limits, as appropriate.
$lim_{x \to \infty} \frac{4 x^{3} - 2 x - 1}{x^{2} - 1}$

e1s2kat26 2021-03-09

Evaluate the following limits. $lim_{(x, y) \to (2, 2)} \frac{y^{2} - 4}{x y - 2 x}$

Limits and continuity help should be approached by turning to arguments and variations of the value. These are always used by engineers and designers, which is why limits and continuity of multiple choice questions can become a nightmare. Things are not that complex in reality. Just see the answers below as there are great solutions that will help you learn. Focus on limits and continuity exercises with answers by taking a look at the questions to compare the analytical part. These samples contained both short and detailed continuity questions and answers, which is why you must depend on your instructions.

Calculus 1

Limits and Continuity Questions and Answers