Limits and Continuity Explained: Expert Help

Recent questions in Limits and continuity

pienelis8n9 2023-02-14

What is $lim_{x \to 4} \frac{x^{4} - 256}{x^{3} - 64}$ ?

cearexceptotob3q 2023-02-14

How to find the limit of $x \tan (\frac{9}{x})$ as x approaches infinity using l'hospital's rule?

inhaltynuaddyh4b 2023-02-14

How to find the limit of $\frac{| x - 7 |}{x - 7}$ as x approaches 7?

Afzal2wl 2023-02-10

How to solve $lim_{x \to a} \frac{f (x) g (a) - f (a) g (x)}{x - a}$ , if f, g have derivative on $x = a$ ?

dsmamacita327zwa 2023-02-10

How to find the limit of $\frac{\sin x}{x}$ as x approaches $\infty$ ?

Corbin Atkinson 2023-02-08

How to find the limit of ${(\cos x)}^{\frac{1}{x^{2}}}$ as x approaches 0?

phasiwedi98z 2023-02-06

What is the limit of $x (\cos (\frac{1}{x}))$ as x approaches infinity?

Corbin Atkinson 2023-02-05

How to find the limit of ${(e^{x} + x)}^{\frac{1}{x}}$ as x approaches 0 using l'hospital's rule?

verfugtg5e 2023-02-02

Is it possible to find the following limit without using l'Hôpital's rule? $lim_{x \to \frac{π}{4}} \frac{\cos x - \frac{1}{\sqrt{2}}}{x - \frac{π}{4}}$

Luis Wolf 2023-02-02

How to find the limit of $x^{\frac{7}{x}}$ as x approaches infinity?

Karson Maddox 2023-01-29

For $x > 0, lim_{x \to 0} [(\sin x)^{\frac{1}{x}} + (\frac{1}{x})^{\sin x}] =$
A)0
B)-1
C)1
D)2

jordancuzwb 2023-01-29

How to find the limit of $\frac{{(8 + h)}^{2} - 64}{h}$ as h approaches 0?

mascaraspx2 2023-01-20

What is the limit as $x \to \infty$ of $e^{- 2 x} \cos x$ ?

Kayley Kidd 2023-01-07

If $f (x) = {\begin{cases} 7 - 4 x, x < 1 \\ x^{2} + 2, x \geq 1 \end{cases}$
then value of $lim_{x \to - 6} f (x)$ is
A)14
B)31
C)it does not exist
D)18

Kristian Combs 2023-01-04

What is the limit of #lim_((x,y)->(0,0))x^2/(x^2+y^2)#?

gibbokf5 2023-01-01

What is the series limit for the Balmer series? (The series limit, like the name suggests, is the last line of the given series - the smallest wavelength that's still part of the same set of spectral lines)
A. 364.6nm
B. 121.6nm
C.656.3nm
D. 385.4nm

colida3956 2022-12-23

Prove the difference of any even integer minus any odd integer is odd.

Kaitlin Jacobson 2022-12-17

Evaluate the common limit
I have to assess some limits without using L'Hopital rule, just by definition. So I got:
$lim_{h \to 0} (\frac{e^{h} - 1}{h}) .$
After evaluating it in a Math app, it states that it's just 1 due to the common limit evaluation, but I don't understand why it's 1.

stellar11185kry 2022-12-14

Why does the study of sampling distributions place such a high value on the central limit theorem?

fabianmartinOTQ 2022-12-04

Consider applying the Limit Comparison Test on $S = \sum_{k = 1}^{\infty} (\frac{3 k}{5 (k - 1) (k + 1)})$
a) Setup and calculate the limit in this test, comparing this series to $\sum_{k = 2}^{\infty} (\frac{1}{k})$
b) Interpret the result of this limit in this test.

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