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
Nitella [24]
3 years ago
9

If the local linear approximation of f(x) = 2cos x + e^2x at x = 2 is used to find the approximation for f(2.1), then the % erro

r of this approximation is?
Mathematics
1 answer:
yKpoI14uk [10]3 years ago
5 0

<u>Answer-</u>

The % error of this approximation is 1.64%

<u>Solution-</u>

Here,

\Rightarrow f(x) = 2\cos x + e^{2x}

\Rightarrow f'(x) = -2\sin x + 2e^{2x}

And,

\Rightarrow f(2) = 2\cos 2 + e^{4}

\Rightarrow f'(2) = -2\sin 2 + 2e^{4}

Taking (2, f(2)) as a point and slope as, f'(2), the function would be,

\Rightarrow y-y_1=m(x-x_1)

\Rightarrow y-(2\cos 2 + e^{4})=(-2\sin 2 + 2e^{4})(x-2)

\Rightarrow y=(-2\sin 2 + 2e^{4})(x-2)+(2\cos 2 + e^{4})

The value of f(2.1) will be

\Rightarrow y=(-2\sin 2 + 2e^{4})(2.1-2)+(2\cos 2 + e^{4})

\Rightarrow y=(-2\sin 2 + 2e^{4})(0.1)+(2\cos 2 + e^{4})

\Rightarrow y=64.5946

According to given function, f(2.1) will be,

\Rightarrow f(2.1) = 2\cos 2.1 + e^{2(2.1)}

\Rightarrow f(2.1) = 65.6766

\therefore \%\ error=\dfrac{65.6766-64.5946}{65.6766}=0.0164=1.64\%

You might be interested in
The management of a restaurant with locations all over the country has developed a new hamburger that researchers believe will s
Sliva [168]

Using sampling concepts, it is found that the best way to perform a randomized experiment with the goal of determining if this new hamburger will sell better than the hamburger that is currently sold is as follows:

Randomly select 40 restaurants, let each one decide if it wants to sell the new hamburger, and compare sales in those restaurants to sales in the restaurants that chose not to sell the new hamburger.

<h3>What is sampling?</h3>

It is is a common statistics practice, when we want to study something from a population, we find a sample of this population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents.

In this problem, a sample of randomly selected restaurants should be taken to sell the new hamburger, and then be compared with the ones who sell the old hamburger to see if sales increased, hence the correct option is:

Randomly select 40 restaurants, let each one decide if it wants to sell the new hamburger, and compare sales in those restaurants to sales in the restaurants that chose not to sell the new hamburger.

More can be learned about sampling concepts at brainly.com/question/25122507

3 0
2 years ago
What is the slope of the graph of y= 3x -<br> 2x–5?<br> b<br> -5<br> 2<br> 3
Ksenya-84 [330]

Answer:

2

Step-by-step explanation:

8 0
3 years ago
Please help this is my 3rd time asking :(​
Ainat [17]

Answer:

$6

Step-by-step explanation:

She bought a toy for 4 dollars, so we need to subtract that from 88. This gives us 84 dolalrs. She bought 8 shirts and 6 pants, which is 14 items total. Divide 88 by 14 and you get 6.

Hope that helps :)

4 0
2 years ago
Read 2 more answers
The total practice time for a football team is 4,380 hours. There are 73 players. How many hours does each player practice?​
VikaD [51]

Each team-mate practices for 60 hours.

You know this because if you divide 4,380 (the total amount of hours) by 73 (the total amount of players) you get 60.

3 0
3 years ago
Convert the following standard form equation into slope-intercept form:<br> 6x + 5y = -15
olasank [31]

Answer:

y=\frac{-6){5}x-3

Step-by-step explanation:

given 6x+5y=-15

   5y=-6x-15

y=\frac{-6}{5}x-\frac{15}{5}

y=\frac{-6}{5}x-3

slope=[tex]\frac{-6}{5}[tex], intercept=-3

6 0
3 years ago
Other questions:
  • Carolina’s family ordered 8 tacos and 1 quesadilla for dinner. The cost for all of tacos was $31.60. The total cost of the meal
    15·2 answers
  • Shreya won 65 pieces of gum playing the bean bag toss. After giving some away she only has 35 remaining. How many does she give
    13·2 answers
  • Caleb earned $49 for working 7 hours. How much would he earn for working 14 hours at the same rate
    5·2 answers
  • Find the value of the linear correlation coefficient r. Round to 3 decimal places. (47, 8), (46, 10), (27, 10)
    12·1 answer
  • Y=6x-11<br> -2-3y=-7 what is the answer?
    7·2 answers
  • HELP!! I will give 30 poins and brainliest to the one who gives me the right answer FIRST!!
    5·1 answer
  • HELP PLEASE ILL MAKE YOU BRILLIANT !?!
    9·1 answer
  • Help plz due very soon
    14·2 answers
  • James invested $1,475 in an account paying 6.25%
    15·1 answer
  • if i walked to my parents house for Thanksgiving and lived 25.6 miles away, and it took me 4 hrs to get there is it true tht my
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!