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Find the following limits or state that they do not exist. Assume a, b, c, and k are fixed real numbers.
$lim_{h \to 0} \frac{\frac{1}{5 + h} - \frac{1}{5}}{h}$

BolkowN 2021-10-23

The process by which we determine limits of rational functions applies equally well to ratios containing nonintegrer or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits
$lim_{x \to - \infty} \frac{4 - 3 x^{3}}{\sqrt{x^{6} + 9}}$

Dottie Parra 2021-10-23

If $f (x) = | x - 1 | + | x + 3 |$ , then discuss the continuity and differentiability of the function at x=-3 and x=1.

glasskerfu 2021-10-22

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

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)
$lim_{x \to - 3} (3 x^{3} + 4 x^{2} - 3)$

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.

Burhan Hopper 2021-10-22

Limit and Continuity Find the limit (if it exists) and discuss the continuity of the function.
$lim_{(x, y) \to (0, 0)} \frac{x^{2} y}{x^{4} + y^{2}}$

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).
$lim_{x \to 1} \frac{| x - 1 |}{x^{2} - 1}$

chillywilly12a 2021-10-21

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

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

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.
$f (x) = x + \sqrt{x - 4}, [4, \infty)$

vazelinahS 2021-10-20

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

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. $f (x) = {(x^{4} + 1)}^{\frac{3}{2}}$

Nann 2021-10-20

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

cistG 2021-10-20

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

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

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.
$lim_{x \to - 3^{\pm}} \frac{x^{2}}{x^{2} - 9}$

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.
$lim_{x \to 0} [e^{\sin (x)} + \frac{x^{2}}{x - 2}]$

The majority of Calculus 1 questions and answers that you will find below should be sufficient for understanding the basic rules that are necessary for problem-solving purposes. Take a look at the original answers, seek math assignment help, and compare them to what you have for your assignment.

If you need any other kind of help for your Calculus 1 tasks, combine several solutions or look at the problem that seems similar to your original assignment. If Math is not your subject per se, start with the most basic problems and proceed with the complex ones.

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