Limits and Continuity Explained: Expert Help

Recent questions in Limits and continuity

Rex Maxwell 2022-03-28

Use L'Hospital Rule to find the limits
$lim_{x \to 0} \frac{\sin m x}{\sin n x}$

Marzadri9lyy 2022-03-28

Evaluate the following limits.
$lim_{θ \to 0} \frac{\sec θ - 1}{θ}$

Coradossi7xod 2022-03-27

compute the limit of
$lim_{x \to \frac{π}{3}} \frac{1 - 2 \cos (x)}{\sin (3 x)}$
I would like to not do a translation with the change of variable $t = x - \frac{π}{3}$

Lesnaoq73 2022-03-27

How can I prove that
$lim_{(x, y) \to (0, 0)} \frac{{| x |}^{\frac{3}{2}} y^{2}}{x^{4} + y^{2}} \to 0$

Erik Cantu 2022-03-27

How can I calculate the following difficult limit: $lim_{x \to \infty} (x + \sin x) \sin \frac{1}{x}$ ?

parksinta8rkv 2022-03-25

How come
$lim_{x \to \infty} x - \ln (1 + e^{x}) = 0$ ?

Caerswso1pc 2022-03-25

How can we find
$lim_{y \to {b}} \frac{y - b}{\ln {y} - \ln {b}}$

smaakt4ucq 2022-03-24

How do I evaluate the limit given ?
$lim_{x \to \infty} \frac{x^{x} - {(x - 1)}^{x}}{x^{x}}$

avalg10o 2022-03-24

How can I find to what this sum converges to?
$\sum_{n = 1}^{\infty} n (n + 1) x^{n}$

Averie Ferguson 2022-03-24

here's a limit that I'm struggling to calculate.
$lim_{x \to 0} \frac{x^{2} \ln x}{\sin x (e^{x} - 1)}$

Zack Mora 2022-03-24

Limit of $\cos (k t + k u x)$ as $k \to 0$
where
$k = 2 \sqrt{1 - a^{2}}$
$u = b (6 - k^{2})$
and a and b are real numbers?

encaderpwp 2022-03-24

Limit of a function as it tends to zero
$lim_{x \to 0} \frac{3 {(\tan 2 x)}^{2}}{2 x^{2}}$
What method is best for solving this? The division by zero is causing me issues when trying to apply Sandwich theorem and/or Algebra of limits.

kembdumatxf 2022-03-23

Limits with variable substitution and Trig
$lim_{x \to 0} \frac{\sin^{2} (3 x)}{x^{2} \cos x} = lim_{u \to 0} \frac{\sin^{2} (u)}{{(\frac{u}{3})}^{2}} = 9 {(lim_{u \to 0} \frac{\sin u}{u})}^{2}$

resaplaha7dl 2022-03-23

limit $lim_{t \to 0} \frac{\sin 3 t}{\tan 2 t}$
I am struggling with this question. I have attempted it, but I keep getting stuck on the following step:
$lim_{t \to 0} \frac{1}{2} \frac{\sin 3 t \cos 2 t}{\sin t \cos t}$

aanvarendbq28 2022-03-23

Limit for $\frac{{(1 - \cos x)}^{(k + x)}}{x}$ when $x \to 0$

Anika Boyd 2022-03-22

Limit $lim_{x \to 0} {\frac{2 x - \sin {x}}{3 x + \sin {x}}}$

Dominique Pace 2022-03-22

Limit $lim_{x \to \frac{π}{3}} \frac{\sin (x - \frac{π}{3})}{1 - 2 \cos {x}}$

avalg10o 2022-03-22

Limit of $lim_{n \to + \infty} {(\cos \frac{x}{n} + \sin \frac{2 x}{n})}^{n}$

Deegan Chase 2022-03-21

Solve this question
$lim_{x \to \infty} {(x + 3)}^{1 + \frac{1}{x}} - x^{1 + \frac{1}{x + 3}}$

dotzis16xd 2022-03-21

Limit $lim_{x \to 0} {\frac{\tan {x} - \sin {x}}{x^{3}}}$
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
$lim_{x \to 0} \frac{\frac{1}{\cos {x}} - 1}{x^{2}}$

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