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
Cerrena [4.2K]
2 years ago
8

Primitive function for: 1. f(x)=4e2x+e−x, sådan att F(0)=2

Mathematics
1 answer:
Free_Kalibri [48]2 years ago
6 0

The primitive function for f(x) = 4e^{2x} + e^{-x} is given by it's indefinite integral.

To calculate it, recall:

\frac{d}{dx}e^{ax}=ae^{ax}

\int c f(x)dx = c\int f(x)dx

Let's begin

\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1}  + c\\

F(x) = 2e^{2x}-e^{-x} +c

To find the costant, we just need to use the fact that F(0)=2

F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3

Therefore,

\boxed{F(x) = 2e^{2x} - e^{-x} -3 }

You might be interested in
What are three different<br>numbers that could by multiplied<br>by a power of ten to equal 7,500?​
stich3 [128]
5,10,and 100 hope this helped
3 0
2 years ago
What is the distance between points A and B?
aleksandr82 [10.1K]
Did you ever get the answer?

3 0
3 years ago
Read 2 more answers
Which of the following is the standard form of 36 / 24​
RSB [31]

Answer:

15 x 10^-1

Step-by-step explanation:

36÷24=1.5

In this case I'm considering 15 as the base of my standard form.

To make 15 a 1.5, you'll have to move from right to left one unit and on the number line moving from the right to left gives you a negative number of units moved

8 0
3 years ago
A certain breed of mouse was introduced onto a small island with an initial population of 320 mice, and scientists estimate that
Viefleur [7K]
Y=2x+320
x being the number of years and 320 being the initial population of mice
7 0
3 years ago
4(x - 2) = 2x + 3(x - 5)
yaroslaw [1]

Answer:

x=7

Step-by-step explanation:

  1. 4(x-2) = 2x+3(x-5)
  2. 4x-8 = 2x+3x-15
  3. 4x-8 = 5x -15
  4. -x = -7
  5. x = 7

8 0
3 years ago
Other questions:
  • The diagram below shows the partial construction of which shape?
    14·2 answers
  • If p. 2 + 2 =4<br> What is p?<br> 2 + 2 4<br> 2 + 2 = 4<br> 2 X 2 4<br> 2 X 2 = 4
    12·2 answers
  • 1. Write a paragraph proof for the following conjecture.
    7·2 answers
  • What are the missing numbers?
    14·1 answer
  • Simplify the function f(x) = 7(). Then answer the questions below. The initial value for the function is . The simplified base f
    7·2 answers
  • -9-13+2+13−9−13+2+13minus, 9, minus, 13, plus, 2, plus, 13.
    5·1 answer
  • What is the cube root of -0.216?<br>​
    15·1 answer
  • A swimming pool is 17.04 metters wide it is didvided into 8 lanes of equal width for swimming laps.How wide is each lane
    6·1 answer
  • Please help me!!! Solve for x<br>​
    5·2 answers
  • Giving brainliest *easy*
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!