All categories

3 years ago

Evaluate the limit using the appropriate properties of limits. (If an answer does not exist, enter DNE.)

Mathematics

1 answer:

Leviafan [203]3 years ago

8 0

Answer:

+infinity, or if there is no such choice, DNE.

Step-by-step explanation:

4x^2 − 3x^2 + x − 3

simplifies to

x^2+x-3

As x-> infinity,

both x^2 and x approach inifinity, therefore

the limit approaches +infinity, or does not exist (DNE)

Generally, it is more indicative to say +infinity or -infinitite, while reserving DNE (does not exist) for incoherent one-sided limits.

You might be interested in

Question 2(Multiple Choice Worth 1 points) (06.01) Solve 2x + 5y = −13 3x − 4y = −8 (4, 1) (−4, 1) (4, −1) (−4, −1)

dlinn [17]

ANSWER

The solution is
$(-4,-1)$

EXPLANATION

The given equations are:

$2x + 5y = - 13...(1)$

and

$3x - 4y = - 8...(2)$

We multiply equation 1 by 3 to get,

$6x + 15y = - 39...(3)$

We multiply equation 2 also by 2 to get,

$6x - 8y = - 16...(4)$

We subtract equation 4 from equation 3 to get,

$23y = - 23$
This implies that,

$y = - 1$

We put this value of y into any of the equations say equation 2

$3x - 4( - 1) = - 8$
Simplify

$3x + 4 = - 8$
Group like terms
$3x = - 8 - 4$
Simplify,

$3x = - 12$

Divide both sides by 3 to get,

$x = - 4$

Therefore the solution is
$(-4,-1)$

The correct answer is option D.

3 0

3 years ago

(a) A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a SRS of 1200 regist

Sladkaya [172]

Answer:

n=9604

Step-by-step explanation:

1) Notation and definitions

$X=620$ number of people that would vote for the Republican candidate

$n=1200$ random sample taken

$\hat p=\frac{620}{1200}=0.517$ estimated proportion of people that would vote for the Republican candidate

$p$ true population proportion of people that would vote for the Republican candidate

Me= 0.01 represent th margin of error.

Confidence =0.95 or 95%

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1- p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

The problem says that we need to use $\hat p =0.05$ , and replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{1.96})^2}=9604$

And rounded we have that n=9604

6 0

2 years ago

The function f(x) = x] is graphed over the interval [-6, 3]. Which translation of the graph has the domain (-3, 6]? 0 A. g(x) =

bezimeni [28]

An interval graph in graphical theory is indeed an undirected graph formed by an interval set just on true line, with a top for every interval as well as an edge between vertex v to intersections. Graph intervals and these graphs are chordal graphs and graphs that are perfect, and the further discussion can be defined as follows:

Given:

$\bold{function\ f(x) = |x|}$