Limits and Continuity Explained: Expert Help

Recent questions in Limits and continuity

Heather Dickson 2022-04-09

How to show that
$lim_{p \to 0} {(\frac{p e^{2 t p}}{1 - e^{2 t p} (1 - p)})}^{k}$

Colten Welch 2022-04-09

How to prove that
$lim \frac{1}{n} \sqrt[n]{(n + 1) (n + 2) \dots 2 n} = \frac{4}{e}$

Aiyana Ayers 2022-04-08

Finding Limit
$lim_{x \to \infty} {(2^{x} + 3^{x} + 5^{x} + 7^{x} + 11^{x} + 13^{x})}^{\frac{1}{x}}$

Jayleen Aguirre 2022-04-08

I'm trying to determine the convergence of this series:
$\sum_{n = 1}^{\infty} (\frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot . . . \frac{2 n - 3}{2 n - 2} \cdot \frac{2 n - 1}{2 n})^{a}$

Henry Winters 2022-04-07

Finding the limit of a sequence
$lim_{n \to \infty} \sqrt[3]{n^{2}} (\sqrt[3]{n + 1} - \sqrt[3]{n})$

Saul Cochran 2022-04-07

Finding $lim_{x \to \infty} (\sqrt{9 x^{2} + 3} - 3 x)$

Justine White 2022-04-07

Find the solution
$lim_{t \to 0} \frac{d^{k - 1}}{{d t}^{k - 1}} {(\frac{t \sqrt{1 + t}}{\log \sqrt{1 + t}})}^{k} = 2 {(k + 2)}^{k - 1}$

Quinn Dean 2022-04-07

i'm having hard time with $lim_{x \to \infty} \frac{x (1 + e^{x^{2}}) \tan x - 2 \sin^{2} x}{x (\tan x - x)}$
i've tried to simplify it using $\cos 2 x$ identity ( $\cos 2 x = 1 - 2 \sin^{2} x \to \cos 2 x - 1 = - 2 \sin^{2} x$ ) ,or tried to break it into 2 different fractions, but i couldn't get it to a point where i could use mclaurin in order to solve the given limit.

Cash Duncan 2022-04-07

I want to show that
$\lim_{n \to \infty} \sqrt{n} (\sqrt[n]{n} - 1) = 0$

Jasiah Vincent 2022-04-07

I need two methods different conclusion.
$lim_{(x, y) \to (0, 0)} \frac{{(x^{3} - y^{2})}^{2}}{x^{4} + y^{4}}$

Briley Cabrera 2022-04-06

Finding: $lim_{x \to - \infty} \frac{6 x^{2} + 5 \cos {π x}}{\sqrt{x^{4} + \sin {5 π x}}}$
I've tried using l'Hospitals rule, however we will alway keep the $\cos (π x)$ expression, as well for $\sin (5 π x)$ . Also, terms do not cancel out with $\sin$ and $π$ since the product with 5

Deacon Simpson 2022-04-06

Finding $lim_{h \to 0} \frac{(\sqrt{9 + h} - 3)}{h}$

zdebe5l8 2022-04-06

I'm trying to solve the following limit:
$lim_{(x, y) \to (2, 1)} \frac{x y {(x - 2)}^{\frac{5}{3}} {(y^{2} - 1)}^{\frac{2}{3}}}{| y | {(x - 2)}^{2} + x^{2} {(y - 1)}^{2}}$

Jasiah Vincent 2022-04-06

I'd love your help with finding the following limit:
$lim_{n \to \infty} \cos (π \sqrt{n^{2} - n})$

Adison Palmer 2022-04-06

I needed to present a method to finding the limit of
$lim_{x \to 0} \frac{9^{x} - 5^{x}}{x}$

Rosa Townsend 2022-04-06

I should prove using the limit definition that
$lim_{x \to 0} x^{\frac{1}{3}} \cos (\frac{1}{x}) = 0$

Pablo Dennis 2022-04-05

Evaluate the limit of
$lim_{x \to \infty} \frac{x - \sqrt{x^{2} + 5 x + 2}}{x - \sqrt{x^{2} + 0.5 x + 1}}$

talpajocotefnf3 2022-04-05

Evaluate $lim_{x \to π} \frac{\sin (m x)}{\sin (n x)}$ where $m, n \in N \cdot$ . At first I thought I could just use the remarkable limit $lim_{x \to 0} \frac{\sin (x)}{x} = 1$ and the answer could just be $\frac{m}{n}$ but this is not the answer.... I mean it's a part of it but I don't understand why.

Destinee Hensley 2022-04-04

Facing difficulty finding limit
$lim_{x \to \infty} {(\frac{x}{x - 1})}^{2 x + 1}$

Rowan Callahan 2022-04-04

Evaluate $lim_{x \to 0^{+}} \frac{\arccos (x) - \frac{π}{2}}{x \ln (x)}$

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