All categories

4 years ago

Lim ln(tan x) as tends to pi/2 from the left

1 answer:

ioda4 years ago

3 0

Let $x=\arctan y$ . Then $\tan x=y$ , and so as $x\to\dfrac\pi2^-$ , you have $y\to+\infty$ . The limit is then equivalent to

$\displaystyle\lim_{x\to\frac\pi2^-}\ln(\tan x)=\lim_{y\to\infty}\ln y=\infty$

You might be interested in

7. Jenny is saving to buy a laptop worth $960. Her parents promise to match every $3 saved

PSYCHO15rus [73]

First off, if you divide $960/$8, you will get 120 “sets” of payment. Multiply this value by the amount of money Jenny is responsible for paying and the amount her parents are responsible for paying to find their total contributions.

a. Jenny will have to pay $600

b. Jenny’s parents will contribute $360 to her new laptop.

8 0

3 years ago

Select the best answer for the question. 8. Evaluate m + n2 if we know m = 2 and n = –2. A. –6 B. 6 C. 8 D. –8

natta225 [31]

M + n² = (2) + (-2)² = 2 + 4 = 6

Answer: 6

3 0

4 years ago

A bank loaned out $14000, part of it at the rate of 9% per year and the rest at 17% per year. If the interest received in one ye

WINSTONCH [101]

Using simple interest, it is found that $13,872 was loaned at 9%.

<h3>Simple Interest</h3>

The amount of money after t years in simple interest is modeled by:

$A(t) = P(1 + rt)$

In which:

P is the initial amount.

r is the interest rate, as a decimal.

The interest earned is:

$I(t) = Prt$

A bank loaned out $14000, in two parts, hence:

$P_2 = 14000 - P_1$

Part of it at the rate of 9% per year and the rest at 17% per year, hence:

$r_1 = 0.09, r_2 = 0.17$

The interest received in one year totaled $2000, hence:

$I_2 = 2000 - I_1$

Then:

$I_1 = 0.09P_1$

$I_2 = 0.17I_2$

$14000 - P_1 = 0.17(2000 - I_1)$

Isolating $I_1$ as a function of $P_1$ , then we can replace on the equation for the first interest.

$14000 - P_1 = 340 - 0.17I_1$

$0.17I_1 = -13660 + P_1$

$I_1 = \frac{P_1 - 13660}{0.17}$

Then:

$I_1 = 0.09P_1$

$\frac{P_1 - 13660}{0.17} = 0.09P_1$

$P_1 - 13660 = 0.0153P_1$

$0.9847P_1 = 13660$

$P_1 = \frac{13660}{0.9847}$

$P_1 = 13872$

$13,872 was loaned at 9%.

To learn more about simple interest, you can take a look at brainly.com/question/25296782

3 0

2 years ago

Suppose Ted, a sociologist, is interested in comparing the amount of time that husbands and wives in the United States each spen

lidiya [134]

Answer:

1. A matched-pairs t-test is valid, despite the sample being a small representation of the population, because the sample is a simple random sample and has a distribution with a single peak.

Step-by-step explanation:

The matched-pairs test is valid, for the reasons given in choice 1. Here's why:

We do have matched pairs, not a 2-sample t-test, because each two are paired by the house they live in. Husband and wife live together: it's safe to pair them. (This rules out option 5.)

Check conditions: The sample is large enough (fulfilling the <u>sample size condition)</u>. The sample data is fairly normal, although we don't know the population data, and the sample size is over 40, so we consider it a fairly large sample (fulfilling the <u>nearly normal condition)</u>. We don't know about outliers, but we'll have to assume Ted doesn't have any, because they aren't mentioned.

8 0

3 years ago

1. In the figure below ∡=153°, ∢=(5+5)°, and ∢=(3+12)°. Find the measure of ∢ and ∢. Show all work.

murzikaleks [220]

Answer: The answer is 10 and 15

7 0

3 years ago