1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fed [463]
2 years ago
13

Use fundamental theorem of calculus to find derivative of the function LOOK AT PHOTO

Mathematics
1 answer:
kykrilka [37]2 years ago
8 0

Let c > 0. Then split the integral at t = c to write

f(x) = \displaystyle \int_{\ln(x)}^{\frac1x} (t + \sin(t)) \, dt = \int_c^{\frac1x} (t + \sin(t)) \, dt - \int_c^{\ln(x)} (t + \sin(t)) \, dt

By the FTC, the derivative is

\displaystyle \frac{df}{dx} = \left(\frac1x + \sin\left(\frac1x\right)\right) \frac{d}{dx}\left[\frac1x\right] - (\ln(x) + \sin(\ln(x))) \frac{d}{dx}\left[\ln(x)\right] \\\\ = -\frac1{x^2} \left(\frac1x + \sin\left(\frac1x\right)\right) - \frac1x (\ln(x) + \sin(\ln(x))) \\\\ = -\frac1{x^3} - \frac{\sin\left(\frac1x\right)}{x^2} - \frac{\ln(x)}x - \frac{\sin(\ln(x))}x \\\\ = -\frac{1 + x\sin\left(\frac1x\right) + x^2\ln(x) + x^2 \sin(\ln(x))}{x^3}

You might be interested in
The amount of corn chips in a 16-ounce bag by the dispensing machine has a normal distribution with a mean of 16.5 ounces and a
Elenna [48]

Answer: 1+1=2

Step-by-step explanation: Imagine you have 1 cookie, and a friend gives you 1 more, that means your total amount of cookies is 2. So that proves that 1+1=2!

8 0
2 years ago
(7.02) classify each sequence as arithmetic, geometric, or neither.
Digiron [165]

Answer:

geometric

arithmetic

arithmetic

Step-by-step explanation:

1.

4/9,4/3,4,12,36

Multiply each term by 3 to get the next term. There is a common ratio between terms, so it geometric.

2.

0,1,2,3,4,5,6

Add 1 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.

3.

-10,-6,-2,2,6,10

Add 4 to each term to get the next term. Since there is a common difference between terms, it is an arithmetic sequence.

6 0
3 years ago
Simplify -15.4/-4…………………….<br> −3.9<br><br> 3.9<br><br> −4.9<br><br> 4.9
Dafna1 [17]
It is 3.9 I hope this will help you
8 0
3 years ago
Answer question below.
12345 [234]

The speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.

<h3>What is speed?</h3>

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

Let the speed of the Elvira be x. Then the speed of the Altheia will be (x - 6).

Let the distance between the coffee shop and Elvira's house be d.

Then the distance between the coffee shop and Altheia's house will be (3.6 - d).

Then we have

x = d / 0.5 ...1

(x - 6) = (3.6 - d) / 0.6 ...2

In solving the equations 1 and 2, we have

x = 6.545 and d = 3.2725 miles

Then the speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.

More about the speed link is given below.

brainly.com/question/7359669

#SPJ1

4 0
2 years ago
I have a question is $20.21 for the gym membership expensive money or not
pav-90 [236]

Answer:

It depends

Step-by-step explanation:

Planet Fitness offers 10 bucks a month but they suck (Lunk alarm + pizza nights? really?) If they offer good services like 24 hour fitness or good equipment then go for it my guy!

3 0
3 years ago
Other questions:
  • I need help with this
    14·2 answers
  • Find the area of the following triangle. Round your answers to the nearest tenth. a = 44 in, b = 66 in, c = 88 in
    12·1 answer
  • I’m literally so confused again omg
    5·1 answer
  • PERMUTATION:
    14·1 answer
  • An athlete ran 1,200 laps around a track over a two month period. He ran 4 times the number of laps in the second month than he
    15·1 answer
  • In the quadratic formula,
    8·1 answer
  • Find the distance of point U(2, 3) from point V(5, 7).​
    8·1 answer
  • Keiko sold 3 less than three-fourths of his sister's sales. Which expression represents what Keiko sold?
    12·2 answers
  • ;-; my last math question can someone please help meh!
    8·1 answer
  • Need help asappppppp
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!