Limits and Continuity Explained: Expert Help

Recent questions in Limits and continuity

Alissa Hutchinson 2022-05-12

I want to find the limit:
$\sqrt{n^{2} + n} - \sqrt[3]{n^{3} - n}$

linziboobeary1o8p 2022-05-11

For any $α \in R$ determine the limit
$lim_{\begin{matrix} > \\ δ \to 0 \end{matrix}} \int_{0}^{2} \frac{1 - x}{δ + x^{α}} d x in [- \infty, + \infty] .$

Jaeden Weaver 2022-05-11

I'm lost on the following problem. I don't know which method to use.
$lim_{x \to \infty} \frac{\sin (\frac{2}{x}) + \frac{2}{x}}{\sin (\frac{1}{x})}$

Eileen Garza 2022-04-28

Limit $lim_{lim} i t s {x \to 0} {\frac{\tan {x} - \sin {x}}{x^{3}}}$
So what I tried is:
$lim_{x \to 0} \frac{\frac{\sin {x}}{\cos {x}} - \sin {x}}{x^{3}} = lim_{x \to 0} \frac{{\sin {x}} (\frac{1}{\cos x} - 1)}{x \cdot x^{2}}$
From here, using the rule $lim_{x \to 0} \frac{\sin {x}}{x} = 1$ it remains to evaluate
$lim_{x \to 0} \frac{\frac{1}{\cos {x}} - 1}{x^{2}}$

chingli20013a1 2022-04-28

Since
$lim_{n \Rightarrow \infty} {(1 + \frac{1}{n})}^{n} = {e}$

Abbigail Robles 2022-04-24

Per the title of this question, how does one go about calculating
$lim_{n \to \infty} \frac{1}{n^{2}} (\ln (\frac{2^{n}}{3^{n}}) + \ln (\frac{5^{n}}{4^{n}}) + \dots + \ln (\frac{{(3 n - 1)}^{n}}{{(n + 2)}^{n}}))$

Sullivan Pearson 2022-04-22

How to find the limit of the sequence with n-th term
$x_{n} = {(\frac{2 n + 3}{n^{2}})}^{n}$

Slade Higgins 2022-04-22

How to calculate the following limit?
$lim_{x \to 0} (\frac{1}{x} + \frac{\ln (1 - x)}{x^{2}})$

et3atissb 2022-04-22

Solve $lim_{x \to 0} (\frac{\sin x}{\sqrt{1 - \cos x}})$

p3sa1bynn 2022-04-21

How to find:
$lim_{x \to \frac{π}{2}} \frac{\tan {2 x}}{x - \frac{π}{2}}$

Ricardo Berger 2022-04-21

How to evaluate $lim_{x \to 0} \frac{x^{2} \sin {\frac{1}{x}}}{\sin x}$

Kailey Perez 2022-04-21

How is
$lim_{h \to 0} \frac{3^{h} - 1}{h} = \ln 3$
evaluated?

Saige Shannon 2022-04-20

How to evaluate
$lim_{x \to \infty} \sqrt[n]{x^{n} + a_{n - 1} x^{n - 1} + \dots + a_{0}} - x$

kadetskihykw 2022-04-20

We are familiar with the classic sum for Euler's constant $γ$ :
$γ = lim_{n \to \infty} (\sum_{k = 1}^{n} \frac{1}{k} - \ln (n))$
But, how is this one derived?:
$γ = lim_{n \to \infty} ({\frac{12}{\sum}}_{k = 1}^{\infty} \frac{{(- 1)}^{k + 1}}{k (2 k)!} n^{2 k} - \ln (n))$

Jordin Olsen 2022-04-19

The limit of $2 \frac{\sin (\frac{M θ_{k}}{2}) \cos (\frac{1}{2} (1 + M) θ_{k})}{\sin (\frac{θ_{k}}{2})}$
where $θ_{k} \in [0, 2 π]$ I can then let $θ_{k} = \frac{2 π k}{N}$ for $k = 0 \dots N$

shaaaaane.shane 2022-04-18

limit of x² + 6x- 7 as x approaches – 2

painter555ui8n 2022-04-17

What is the best method to solve the limit $lim_{x \to \infty} {(1 + \sin \frac{2}{x^{2}})}^{x^{2}}$ ?

Sebastian Fox 2022-04-16

Knowing that
$lim_{x \to a} \frac{x^{2} - \sqrt{a^{3} x}}{\sqrt{a x} - a} = 12$
Find out a.

Trent Fuller 2022-04-15

Find limit of $lim_{x \to 0} \frac{\sin^{200} (x)}{x^{199} \sin (4 x)}$ , if it exists

Hallie Watts 2022-04-14

Is there a way to evaluate this limit:
$lim_{x \to 0} \frac{\sin (e^{\tan^{2} x} - 1)}{\cos^{\frac{3}{5}} (x) - \cos (x)}$

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