Limits and Continuity Explained: Expert Help

Recent questions in Limits and continuity

Alyce Wilkinson 2021-10-22

Solve the limit:
$lim_{x \to 0} \frac{{(3 + x)}^{2} - 9}{x}$

nitraiddQ 2021-10-22

Determine the limit of each function analytically. Show neat and complete solution. (hint: some of the items need to be factored or rationalized for the limits to exist)
$lim_{x \to - 3} (3 x^{3} + 4 x^{2} - 3)$

glasskerfu 2021-10-22

Calculate the following limits, if they exist, by using a combination of polar coordinates and de L’Hopital rule.
$lim_{(x, y) \to (0, 0)} \frac{\arctan (x^{2} + y^{2})}{x^{2} + y^{2}}$

Chaya Galloway 2021-10-22

Use L'Hospital Rule to evaluate $lim_{x \to \infty} \frac{2 x^{2} + 3 x}{2 x^{3} + 3 x + 7}$ , Then determine the limit using limit laws and commonly known limits.

Chaya Galloway 2021-10-21

To demonstrate that the function is continuous on the given interval, use the definition of continuity and the characteristics of limits.
$f (x) = x + \sqrt{x - 4}, [4, \infty)$

Reggie 2021-10-21

Evaluate each limit if it exists. Show all work and give evidence of reasoning. If a limit does not exist, identify in what way it does not exist ( $\infty, - \infty,$ DNE).
$lim_{x \to 1} \frac{| x - 1 |}{x^{2} - 1}$

Line 2021-10-21

Use continuity to evaluate the limit
$lim_{x \to 4} \frac{12 + \sqrt{x}}{\sqrt{12 + x}}$
To find:
a) Domain of Numerator of function
b) Domain of denominator of the function
c) limit

chillywilly12a 2021-10-21

Evaluate the following limits.
$lim_{x \to \frac{π}{2}} (x - \frac{π}{2}) \sec (x)$

pedzenekO 2021-10-20

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.
$lim_{x \to 1^{\pm}} \frac{x^{5} + x - 2}{x^{2} + x - 2}$

sjeikdom0 2021-10-20

Use limit theorems as neede to evaluate each of the following limits
b) $lim_{x \to 2^{-}} \frac{3 x^{2} - 5 x - 2}{| x^{3} - 8 |}$

melodykap 2021-10-20

Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers.
$lim_{x \to 4} \frac{31 x - 42 \sqrt{x + 5}}{3 - \sqrt{x + 5}}$

e1s2kat26 2021-10-20

Evaluate the following limits.
a) $lim_{x \to \infty} (- 40 x^{2} - 36 x^{3})$
b) $lim_{x \to - \infty} (- 40 x^{2} - 36 x^{3})$

lwfrgin 2021-10-20

Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are $\infty$ or $- \infty$ , and describe the corresponding vertical asymptote.
$lim_{x \to - 3^{\pm}} \frac{x^{2}}{x^{2} - 9}$

Nann 2021-10-20

Evaluate the following limits, where c and k are constants.
$lim_{x \to 2} {(5 x - 6)}^{\frac{3}{2}}$

vazelinahS 2021-10-20

Determine the domain of the function and prove that it is continuous on its domain using the Laws of Continuity and the facts quoted in this section. $f (x) = {(x^{4} + 1)}^{\frac{3}{2}}$

vazelinahS 2021-10-20

Evaluate $lim_{x \to \infty} \frac{5 x^{2} - 3 x}{9 + e^{x}}$

UkusakazaL 2021-10-20

Show that the limit leads to an indeterminate form. Then carry out the two-step procedure: Transform the function algebraically and evaluate using continuity.
$lim_{h \to 3} \frac{9 - h^{2}}{h - 3}$

Wribreeminsl 2021-10-20

Use and cite the continuity theorems presented in lecture to find and justify the limit.
$lim_{x \to 0} [e^{\sin (x)} + \frac{x^{2}}{x - 2}]$

cistG 2021-10-20

Find the limit, if it exists, or show that the limits does not exist.
$lim_{(x, y) \to (3 π, 2 π)} x y \cos (x - 2 y)$ .

Nann 2021-10-19

A tank initially contains 120 L of pure water. A mixture containing a concentration of γ g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves the tank at the same rate. Find an expression in terms of γ for the amount of salt in the tank at any time t. Also ﬁnd the limiting amount of salt in the tank as $t \to \infty$

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Calculus 1

Limits and Continuity Questions and Answers