Limits and Continuity Explained: Expert Help

Recent questions in Limits and continuity

zachutnat4o 2021-11-15

Let
f(x,y)= ${\begin{cases} \frac{x y}{2 x^{2} + 3 y^{2}}, (x, y) \neq (0, 0) \\ 0, (x, y) = (0, 0) \end{cases}$
Discuss continuity of f(x,y) and existence of first order partial derivateves.

Tammy Fisher 2021-11-14

Find the limit (if it exists).
$lim_{x \to 7^{+}} \ln (x - 7)$

urca3m403 2021-11-14

If $4 \leq x g (x) \leq 2 x^{4} - 2 x^{2} + 4$ for all x, evaluate $lim_{x \to 1} g (x)$

jeliceg2 2021-11-13

Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why. lim x tends to 0
$e^{x} - 1 - \frac{x}{x^{2}}$

Minerva Kline 2021-11-12

Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are oo or -oo, and describe the corresponding vertical asymptote.
$lim_{x \to 0^{\pm}} \frac{x - \sin | x |}{x^{3}}$

sputavanomr 2021-11-11

Discuss the continuity and differentiability of the function g(t) at t=1, where
g(t)= ${\begin{cases} t^{3}, & t \leq 1 \\ t, & t > 1 \end{cases}$

alesterp 2021-11-10

Find the limits:
$lim_{x \to \infty} \sqrt{\frac{8 x^{2} - 3}{2 x^{2} + x}}$

Emeli Hagan 2021-11-09

Derivatives from limits The following limits represent ƒ′(a)
for some function f and some real number a.
a. Find a possible function f and number a.
b. Evaluate the limit by computing f'(a)
$lim_{x \to 0} \frac{e^{x} - 1}{x}$

Brennan Flores 2021-11-09

Find the following:
$lim_{x \to - 2} (\frac{1}{x^{2}} + \frac{1}{x^{3} + 4})$
Explain your answers using the continuity property of the addition, subtraction, multiplication, and division.

facas9 2021-11-09

Calculating limits. Determine the following limits.
$lim_{x \to - \infty} (| x - 1 | + x)$ and $lim_{x \to \infty} (| x - 1 | + x)$

CoormaBak9 2021-11-09

Define the function:
$f (x) = \frac{1 - \arctan x}{\sin (x) - \cos (x)}$
and compute $lim_{x \to \sqrt{3}} f (x)$ . Once again, we have not given you directions on computing limits so use one of the methods outlined above to access the help files and determine how to do this

glamrockqueen7 2021-11-08

Use l'Hospital Rule to evaluate $lim_{x \to \infty} \frac{2 x^{2} - 5 x}{9 x^{2} + 7}$ , Then determine the limit using limit laws and commonly known limits.

beljuA 2021-11-08

Using:
$lim_{x \to 4} f (x) = 3$ and $lim_{x \to 4} g (x) = 7$

bobbie71G 2021-11-08

Identify the location of any discontinuities of f (x) attached
For each discontinuity, determine the type of discontinuity by evaluating the left- and right-side limits.
$f (x) = \frac{x - 1}{x^{2} + x}$

fortdefruitI 2021-11-08

Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are ∞ or -∞, and describe the corresponding vertical asymptote.
$lim_{x \to 2^{\pm}} \cos (\frac{π}{2} (x - [x]))$

cistG 2021-11-07

Evaluate the following limits. Some require Squeeze Theorem some do not. If you are using Squeeze Theorem, make sure it is clear how you bounded your function and why Squeeze Theorem applies.
$lim_{x \to 0} 3 x^{4} e^{\cos (\frac{1}{x^{2}})}$

Ramsey 2021-11-07

Calculating limits The following limits are the derivatives of a composite function g at a point a.
a. Find a possible function g and number a.
b. Use the Chain Rule to find each limit. Verify your answer by using a calculator
$lim_{x \to 0} \frac{\sqrt{4 + \sin x} - 2}{x}$

geduiwelh 2021-11-07

Find the limit
$lim_{x \to 7} \frac{x^{2} + 2 x}{x^{2} - 41}$
and explain your answer using the continuity property of the addition, subtraction, multiplication, and division.

Kaycee Roche 2021-11-06

Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are ∞ or −∞, and describe the corresponding vertical asymptote.
$lim_{x \to - 2^{\pm}} \frac{4 x^{2} + 7}{x^{3} + 8}$

abondantQ 2021-11-06

Discuss the continuity of the function $f (x) = {\begin{cases} x^{2} - 3 x & i f & x < 2 \\ 2 x + 4 & i f & x \geq 2 \end{cases}$
on the open interval $0 \leq x \leq 2$

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