Limits and Continuity Explained: Expert Help

Recent questions in Limits and continuity

Aileen Rogers 2022-04-14

Find the limit of the complex function.
$lim_{x \to a} {(2 - \frac{x}{a})}^{(\tan \frac{π x}{2 a})}$
I have simplified this limit to this extent :
$e^{lim_{x \to a} ((1 - \frac{x}{a}) (\tan \frac{π x}{2 a}))}$
I don't know how to simplify the limit after that.

zdebe5l8 2022-04-14

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

Destinee Bryan 2022-04-14

Find $lim_{n \to \infty} n (\cos (\frac{1}{\sqrt{n}}) - 1)$

Karlie Mays 2022-04-13

Is $lim_{n \to \infty} \frac{1}{n} (\cos {\frac{π}{n}} + \cos {\frac{2 π}{n}} + \dots + \cos {\frac{n π}{n}})$ a Riemann sum?

Colten Welch 2022-04-13

Find the limit of $\frac{\cos (3 x) - 1}{\sin (2 x) \tan (3 x)}$ without L'Hospital technique

Camila Glenn 2022-04-13

Find limit of $lim_{x \to 0} (\sqrt{x^{6} + 5 x^{4} + 7 x^{2}} \cos (1 + x^{- 1000}))$ if it exists

Aliana Alvarez 2022-04-12

Find the limit of a function
$lim_{x \to 3} \frac{\sqrt{3 x} - 3}{\sqrt{2 x - 4} - \sqrt{2}}$

Aileen Rogers 2022-04-12

Find the limit of ${(e^{2 x} + 1)}^{\frac{1}{x}}$

Joaquin Salas 2022-04-12

Find the limit of $n^{2} \log^{n} (1 - \frac{c \log n}{n})$

Ormezzani6cuu 2022-04-12

Find $a, r > 0$ such that
$lim_{n \to \infty} n^{r} \cdot \frac{1}{2} \cdot \frac{3}{4} \dots \frac{2 n - 1}{2 n} = a$

Ormezzani6cuu 2022-04-12

find limit of a sequence
I have a sequence:
$X_{n} = \cos ({(\frac{3^{n} + π^{n}}{3^{n} + {(π - \frac{1}{4})}^{n}})}^{\frac{1}{n}})$
I have to find the limit when $n \to \infty$ where $n \in N$ .
Which is the best way to find the answer ?

Aliana Alvarez 2022-04-11

trigonometry limits when x approaches zero
a) $lim_{x \to 0} \frac{x}{\sin x} = 1$
b) $lim_{x \to 0} \frac{\sin x}{x} = 1$
Is a) and b) true?
Because if I try to apply this to $lim_{x \to 0} \sin 17 \frac{x}{x}$ , my answer is 17, not 1

Jazmin Strong 2022-04-11

The set of all points of discontinuity of the function $f (x) = lim_{n \to \infty} \sin^{2 n} (π \frac{x}{2})$

Destinee Bryan 2022-04-10

Two six-sided dice are rolled and their product is taken. How many elements are in the subset of even numbers?

Jakobe Norton 2022-04-10

Trying to solve:
$lim_{x \to \infty} \frac{\ln^{1000} x}{x^{5}}$

Frances Simon 2022-04-10

Trigonometry limit's proof: $lim_{x \to 0} \frac{\sin (x) + \sin (2 x) + \dots + \sin (k x)}{x} = \frac{k (k + 1)}{2}$
I tried to split up the fraction and multiple-divide every new fraction with its x factor but didn't work out. ex:
$lim_{x \to 0} \frac{\sin (2 x)}{x} = lim_{x \to 0} \frac{\sin (2 x) \cdot 2}{2 \cdot x} = 2$

George Michael 2022-04-10

The problem is:
$lim_{(x, y, z) \to (0, 0, 0)} \frac{x y + 2 y z + 3 x z}{x^{2} + 4 y^{2} + 9 z^{2}}$

garcialdaria2zky1 2022-04-10

I was wondering whether this limit converges to zero:
$lim_{n \to \infty} \frac{\sum_{i = 0}^{n} \sqrt{i}}{n^{2}} = 0$

Malachi Mullins 2022-04-09

I'm having trouble solving this limit:
$lim_{x \to - 2^{-}} \frac{1}{{(x + 2)}^{2}}$

Jayleen Aguirre 2022-04-09

I would like to evaluate the limit
$lim_{h \to 0} (\frac{1 - \cos {5 h}}{\cos {7 h} - 1})$
I'm having a hard time doing this, however. When you try evaluating directly, of course, it comes out in indeterminate form. I tried using the identity
$lim_{h \to 0} (\frac{1 - \cos h}{h}) = 0$
by breaking the limit up into two limits, by dividing and multiplying by h, but that only takes me to $0 \cdot 10$ . What can I do to evaluate this?

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