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3 years ago

Let F of x equals the integral from 1 to 3 times x of the natural logarithm of t squared. Use your calculator to find F″(1).

2 answers:

eduard3 years ago

7 0

Reading that as

$F(x)=\displaystyle\int_1^{3x}(\ln t)^2\,\mathrm dt$

By the fundamental theorem of calculus, the first derivative is

$F'(x)=3(\ln(3x))^2$

and so the second derivative would be

$F''(x)=\dfrac{6\ln(3x)}x$

which means

$F''(1)=6\ln3$

Sindrei [870]3 years ago

5 0

Answer: answer is 6

Step-by-step explanation:

Took the test and got it correct !

You might be interested in

Which ratio can form a proportion with 4/8

photoshop1234 [79]

The answer will be 1/2

3 0

3 years ago

Read 2 more answers

Joaquin writes the following list of numbers.

swat32

From the given list of numbers, the numbers that are:

rational are 26, -3/2, 0, and 9.

irrational are 5.737737773..., and √45.

Any number that can be written in the form of p/q, where p and q are integers, and q ≠ 0, are called rational numbers.

All terminating and non-terminating recurring decimals are rational numbers.

All the numbers that cannot be represented in the rational form of p/q are irrational numbers.

All non-terminating non-recurring decimals are irrational.

All square roots of imperfect square numbers, that is, surds, are irrational numbers.

In the question, we are asked to classify the given list of numbers into rational and irrational numbers.

5.737737773...: It is an irrational number, since its a non-terminating non-recurring decimal.
26: It is rational as it can be represented in the p/q form (26/1).
√45: It is irrational as it is a square root of an imperfect square number, that is, it is a surd.
-3/2: It is rational as it is in the form p/q.
0: It is rational as it can be represented in the p/q form (0/1).
9: It is rational as it can be represented in the p/q form (9/1).

Thus, from the given list of numbers, the numbers that are:

rational are 26, -3/2, 0, and 9.

irrational are 5.737737773..., and √45.

Learn more about rational and irrational numbers at

brainly.com/question/14994517

#SPJ9

The provided question is incorrect. The correct question is:

Joaquin writes the following list of numbers.

5.737737773..., 26, √45, -3/2, 0, 9.

Which numbers are rational?

Which numbers are irrational?

6 0

2 years ago

A/ab-bsquare + b/ab-asquare?

lord [1]

Answer:

$\dfrac{(a+b)}{ab}$

Step-by-step explanation:

The given expression is :

$\dfrac{a}{ab-b^2}+\dfrac{b}{ab-a^2}$

It can be solved as follows :

$\dfrac{a}{ab-b^2}+\dfrac{b}{ab-a^2}=\dfrac{a}{b(a-b)}+\dfrac{b}{a(b-a)}\\\\=\dfrac{a}{b(a-b)}+\dfrac{b}{-a(-b+a)}\\\\=\dfrac{1}{a-b}(\dfrac{a}{b}-\dfrac{b}{a})\\\\=\dfrac{a^2-b^2}{ab(a-b)}\\\\=\dfrac{(a-b)(a+b)}{ab(a-b)}\\\\=\dfrac{(a+b)}{ab}$

So, the solution of the given expression is equal to $\dfrac{(a+b)}{ab}$ .

7 0

3 years ago

Y’all i’m stuck help me

Tamiku [17]

<h3>Answer: Choice E</h3>

======================================================

Explanation:

Think of 25 as 25/1 and 5 as 5/1

Choice E is really saying $\frac{25}{1} \div \frac{5}{1}$ which becomes $\frac{25}{1} \times \frac{1}{5}$ . Note the second fraction flips and we change to a multiplication sign.

------------

Or you could think of it like this:

$25 \times \frac{1}{5} = \frac{25}{1} \times \frac{1}{5} = \frac{25*1}{1*5} = \frac{25}{5} = 25 \div 5$

to help see why the answer is E.

4 0

3 years ago

Read 2 more answers

One leg of a right triangle has a length of 5m. The other sides have lengths that are consecutive integers. Find these lengths.

pickupchik [31]

The lengths of the other two sides of the right triangle are 12 and 13

<h3>Pythagorean theorem </h3>

From the question, we are to determine the lengths of the other sides of the triangle

From the given information,

The other sides have lengths that are consecutive integers

Thus,

If the length of the other side is x

Then,

The hypotenuse will be x + 1

By the <em>Pythagorean theorem</em>, we can write that

(x+1)² = x² + 5²

(x+1)(x+1) = x² + 25

x² + x + x + 1 = x² + 25

x² - x² + x + x = 25 - 1

2x = 24

x = 24/2

x = 12

∴ The other leg of the right triangle is 12

Hypotenuse = x + 1 = 12 + 1 = 13

Hence, the lengths of the other two sides are 12 and 13

Learn more on Pythagorean theorem here: brainly.com/question/4584452

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7 0

2 years ago