Limits and Continuity Explained: Expert Help

Recent questions in Limits and continuity

smileycellist2 2021-10-30

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)
$lim_{x \to - 4} \frac{{(x + 4)}^{2}}{x^{2} - 16}$

Anonym 2021-10-30

Find the following limits or state that they do not exist.
$lim_{x \to 4} \frac{x^{2} - 16}{4 - x}$

babeeb0oL 2021-10-30

Evaluate each limit and justify your answer.
$lim_{x \to 1} {(\frac{x + 5}{x + 2})}^{4}$

Lipossig 2021-10-30

Compute the following using limits. Show all work using calculus
$lim_{x \to \infty} x \sin (\frac{π}{x})$

Burhan Hopper 2021-10-29

Evaluate the following limits.
$lim_{x \to \infty} {(2 + \frac{4}{x})}^{2 x}$

he298c 2021-10-29

Find the limits (that is, end behaviors) below.
$lim_{x \to \infty} \frac{- 2 x (x^{2} + 4)}{- 7 - 7 x^{4}}$

Tammy Todd 2021-10-29

Evaluate the given limits.
a) $lim_{x \to 0} (2 \sin x + e^{x})$
b) $lim_{x \to 2} \frac{x - 2}{x^{2} - 4}$

nitraiddQ 2021-10-29

Discuss the continuity and differentiability of the function $f (x, y) = \frac{x^{2} y}{x^{2} + y^{2}}$ at the point (0,0)

nagasenaz 2021-10-29

Continuity and limts: Show a function is continuous at a
$f (x) = {(x + 2 x^{3})}^{4}, a = - 1$

babeeb0oL 2021-10-29

Analyze general properties of continuity and discuss the continuity of the following.
$f (x) = \sqrt{3} {x^{2} - 9}$

Amari Flowers 2021-10-29

Use the definition of continuity and the properties of limits to show that the function
$f (x) = x \sqrt{16 - x^{2}}$ is continuous on the interval [-4,4]

Tammy Todd 2021-10-28

The limit represents f'(c) for a function f and a number c. Find f and c.
$lim 2 \sqrt{x} - \frac{6}{x - 9}$
$x \to 9$

Bergen 2021-10-28

Evaluate $lim_{x \to 0^{+}} \frac{1}{x} - \frac{1}{e^{x} - 1}$

Emeli Hagan 2021-10-28

Evaluate the following limits.
a) $lim_{x \to \infty} \frac{\sqrt{7 + 9 x^{2}}}{11 + 7 x}$
b) $lim_{x \to - \infty} \frac{\sqrt{7 + 9 x^{2}}}{11 + 7 x}$

CoormaBak9 2021-10-28

Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers.
$lim_{t \to 3} \sqrt{3} {t^{2} - 10}$

ka1leE 2021-10-28

Show that the limit leads to an indeterminate form. Then carry out the two-step procedure: Transform the function algebraically and evaluate using continuity.
$lim_{x \to - 1} \frac{x^{2} + 2 x + 1}{x + 1}$

texelaare 2021-10-28

Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers.
$lim_{x \to 4} \frac{\frac{1}{x} - \frac{1}{4}}{x - 4}$

Bergen 2021-10-27

Evaluate the following limits.
a) $lim_{x \to {\frac{3}{2}}^{+}} \frac{18 x}{3 - 2 x}$
b) $lim_{x \to {\frac{3}{2}}^{-}} \frac{18 x}{3 - 2 x}$

OlmekinjP 2021-10-27

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

Anonym 2021-10-26

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
$f (x) = {(x + 2 x^{3})}^{4}, a = - 1$

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