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
oksano4ka [1.4K]
3 years ago
13

How do you use the limit definition of the derivative to find the derivative of f(x)=1/x?

Mathematics
1 answer:
guapka [62]3 years ago
6 0
Example 1. Let us start with the functionf(x) = x2. We have 




So 




which means f '(a) = 2a.

What about the derivative of f(x) = xn. Similar calculations, using the binomial expansion for (x+y)n (Pascal's Triangle), yield 




You might be interested in
Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of
Tom [10]

Question:

Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of scale below.

\frac{42m}{7}/{\frac{24m}{7} = \frac{6}{4}

Which is Abel’s error?

Abel should have written the ratio as 24 metres/7 metres

Abel should have written the ratio as 24 metres/42 metres

Abel should have divided both numbers by 6.

Abel should have divided both numbers by 4.

Answer:

Abel should have divided both numbers by 6.

Step-by-step explanation:

Given

Measured Length of backyard = 42m

Actual Length of backyard = 24m

Measured Ratio: \frac{42m}{7}/{\frac{24m}{7} = \frac{6}{4}

Required

Error in calculation of measured ratio

From Abel's calculation:

It can be observed that He divided both numbers by 7

Though 42/7 = 6 but that's not so for 24/7

24/7≠4;

Instead 24/7 = 3.43 (Approximated)

To get the actual ration, he has to divide both numbers by the highest common factor

The common factors of 42 and 24 include 2,3,6 of which the highest is 6

Hence; HCF of 42 and 24 = 6

So, we can conclude that the error in his calculation is having not dividing both numbers by 6

7 0
4 years ago
Read 2 more answers
100 is the regular price if you buy one and get the other half price. Explain how this different from getting a 50% discount?
Vinvika [58]
100 = x + x/2

3x/2 = 100

x = 200/3

if there was 50% discount:

buying 1 would be $33.33

buying 2 would be $66.67
4 0
3 years ago
A. y= -4/5x+ 5/4 <br> B. y= -4/5x+ 3/2<br> C. y= -5/4x+ 3/2<br> D. y= -5/4x+ 5/4
Effectus [21]
The answer is C and here are the steps

7 0
3 years ago
What is the midpoint of a segment with These endpoints (-12,-3) and (3,-8)
Savatey [412]

Answer:

(\frac{-9}{2},\frac{11}{2})

Step-by-step explanation:

you have to use the midpoint formula which is

(\frac{x1+x2}{2},\frac{y1+y2}{2})

so you plug your numbers in

(\frac{-12+3}{2},\frac{-3+-8}{2})

Add the tops

(\frac{-9}{2} ,\frac{-11}{2} )

if possible simplify

and that is your answer

8 0
2 years ago
Simplify (5n^4)^-3. Assume n = 0.
denpristay [2]

Answer:

0

Step-by-step explanation:

5*0=0

0^4=0

0^-3=0

8 0
3 years ago
Read 2 more answers
Other questions:
  • Rent, salaries, and other fixed costs are $100,000. The gross profit on each unit of sales is $10. How many units must the compa
    13·1 answer
  • Which expression is equivalent to 18 - 7?
    10·1 answer
  • PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!<br><br> What is the value of x?
    10·1 answer
  • I am a little confused: One method you can use to determine whether a triangle is a right triangle, given three side lengths, is
    10·2 answers
  • A circle with radius of 1  cm sits inside a 11 cm x 12 cm rectangle
    9·2 answers
  • Find the LCD to each the fractions and then add them together 1/4 + 2/5 + 1/3
    13·2 answers
  • A square has a perimeter of 4 cm. What is the length of each side?
    9·2 answers
  • What is the reciprocal of 453463.432849
    11·1 answer
  • PLEASE ANSWER! 15 POINTS
    5·1 answer
  • If two sides of a triangle measure 18 centimeters and 22 centimeters what could be the measure of the third side
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!