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
hichkok12 [17]
2 years ago
7

A differentiable function f has the property that f(x + y) = f(x) + f(y) 1 − f(x)f(y) holds for all x, y in the domain of f. It

is known also that lim x→ 0 f(x) = 0, lim x →0 f(x) x = 5. (i) Use the definition of the derivative of f to determine f ′ (x) in terms of f(x).

Mathematics
1 answer:
Fantom [35]2 years ago
3 0

Answer:

f'(x) = 5[1 + f²(x)]

Step-by-step explanation:

By definition, f'(x) = lim h => 0 {[f(x + h) - f(x)]/h}

This was used, together with the given limits:

lim x => 0 f(x) = 0

lim x => 0 f(x)/x = 5,

to determine the derivative of the given function:

f(x + y) = [f(x) + f(y)]/[1 - f(x)f(y)].

The workings are shown in the attachments.

You might be interested in
Mike Alyssa Sara and Jessica each have 6 baseball cards how many baseball cards do they have in all​
stepan [7]

Answer:

12

Step-by-step explanation:

its 12

3 0
3 years ago
Read 2 more answers
What is the slope of a line parallel to the line that passes through (4, -3) and (3, -1)?
FinnZ [79.3K]

Answer:

-2

Step-by-step explanation:

find rise over run with y1-y2/x1-x2 = -2/1 = -2

5 0
3 years ago
A painter charges by the square foot and charges you $1,875 to paint a 750 square foot rental house. If you need 1300 square foo
Stella [2.4K]

In this question , it is given that

A painter charges by the square foot and charges you $1,875 to paint a 750 square foot rental house.

For 750 square foot, he charges $1875.

So for 1 square foot, he charges

= \frac{1875}{750} = $2.50 \ \per \ square \ foot

And for 1300 square foot, he charges

= 2.50*1300 = $3250

3 0
3 years ago
Suppose you accumulated $500,000, perhaps from many years of saving. You put the money in a savings plan earning 6% compounded m
nata0808 [166]
The monthly interest rate is 6%/12 = 0.5%. The interest earned each month is
0.005*$500,000 = $2500

You can withdraw $2500 each month without disturbing the principal amount.
3 0
3 years ago
Find A n B if A={3,6,9,12} and B={2,4,6,8,10,12}
SashulF [63]
A ∩ B = {3, 6, 9, 12} ∩ {2, 4, 6, 8, 10, 12}
= {6, 12}
3 0
3 years ago
Read 2 more answers
Other questions:
  • Find the area of the following shape. you must show all work to receive credit
    11·1 answer
  • The ratio of sides of 2 similar cubes is 3:4. Larger cube has a volume of 1728 cubic meters. What is the volume of the smaller c
    14·1 answer
  • Yeah, it's really late at night and I can't think...hah..help
    7·2 answers
  • Which unit represents 100 meters?<br> hectometer<br> kilometer<br> decameter<br> centimeter
    8·2 answers
  • What is the solution if any, to the inequality 3-l4-nl&gt;1?
    5·1 answer
  • Umer is 5 years older than Abdullah. If the product of their ages is 234. How old is<br> Abdullah?
    6·1 answer
  • LCM of 3,5,8,4 in explanation​
    9·1 answer
  • 3) A product is marked down 15%; the sale price is $127.46. What was the<br> original price?
    10·2 answers
  • what good qualities of a dress maker when she fulfills commitment and abides by what is agreed upon by the customer​
    15·1 answer
  • Is the triangle with the lengths of 6, 7, and 9 a right triangle? (show work using Pythagorean theorem) Need to write the number
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!