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
Dmitriy789 [7]
3 years ago
15

Find lim ?x approaches 0 f(x+?x)-f(x)/?x where f(x) = 4x-3

Mathematics
1 answer:
Whitepunk [10]3 years ago
7 0

If f(x)=4x-3:

\displaystyle\lim_{\Delta x\to0}\frac{(4(x+\Delta x)-3)-(4x-3)}{\Delta x}=\lim_{\Delta x\to0}\frac{4\Delta x}{\Delta x}=4

If f(x)=4x^{-3}:

\displaystyle\lim_{\Delta x\to0}\frac{\frac4{(x+\Delta x)^3}-\frac4{x^3}}{\Delta x}=\lim_{\Delta x\to0}\frac{\frac{4x^3-4(x+\Delta x)^3}{x^3(x+\Delta x)^3}}{\Delta x}

\displaystyle=\lim_{\Delta x\to0}\frac{4x^3-4(x^3+3x^2\Delta x+3x(\Delta x)^2+(\Delta x)^3)}{x^3\Delta x(x+\Delta x)^3}

\displaystyle=\lim_{\Delta x\to0}\frac{-12x^2\Delta x-12x(\Delta x)^2-4(\Delta x)^3}{x^3\Delta x(x+\Delta x)^3}=-\frac{12}{x^4}

You might be interested in
An angle's initial ray points in the 3-o'clock direction and its terminal ray rotates CCW. Let θ represent the angle's varying m
Alexxandr [17]

Answer:

0.546 , -4.71

Step-by-step explanation:

Given:

An angle's initial ray points in the 3-o'clock direction and its terminal ray rotates counter -clock wise.

Here, Slope = tan\theta

If θ = 0.5

Then, Slope = tan(θ) = tan(0.5) = 0.546

If θ = 1.78

Then, Slope = tan(θ) = tan(1.78) = - 4.71

The expression (in terms of θ) that represents the varying slope of the terminal ray.

Slope = m = tanθ, where θ is the varying angle

7 0
3 years ago
Arrange 439.216 439.126 439.612 439.261 in decreasing order
Thepotemich [5.8K]

hi <3

439.612, 439.261, 439.216, 439.126

hope this helps :)

7 0
2 years ago
Read 2 more answers
4/ 5 ÷ 5/4 will give you<br><br> 1<br> 16/25<br> 1 whole 9 / 25
vova2212 [387]

Answer:

16/25

Step-by-step explanation:

first do keep change flip

4/5 × 4/5

16/25

6 0
3 years ago
Read 2 more answers
What's the steps used to solve modeling problems in the correct order​
Stolb23 [73]

Answer:

see below

Step-by-step explanation:

The first step is to read the problem

Then you need to make a plan

Implement the plan

Then evaluate the answer to see if it makes sense

6 0
3 years ago
What is an equation of the line that passes through the point (-4, -6) and is
const2013 [10]
Answer:y=2/3x-10/3
- 4/-6 is 4/6 so m is 4/6 then fill in the x and y variables in y=Mx+b solve for b then start plotting the equation of the line to check and you get your answer

I think this is the answer you might need to check again with more people
8 0
2 years ago
Read 2 more answers
Other questions:
  • 6.5.6. Suppose a sufficient statistic exists for the parameter θ. Use Theorem 5.6.1 to show that the critical region of a likeli
    15·1 answer
  • Please help with this
    8·1 answer
  • Point A is located at (0, -2) and is rotated 180°. What are the coordinates of point A'?
    8·2 answers
  • if a rocket that is launched into space travels at 300 feet per second then how fast is the rocket traveling in yards per minute
    15·2 answers
  • 2/3 x + 1/2 equals 3/4 + 5/3 ​
    6·1 answer
  • Help Please 100 point's + Brainly.est 8th grade Math Look at the photos below and answer them PLEASE
    15·2 answers
  • Use the verbs in the word bank to complete the sentences. Remember that you will need to put the verb in the correct form. Watch
    11·2 answers
  • Find the denominator that names a fraction equivalent to 3/2
    9·1 answer
  • Steve has a piece of fishing line measuring 6 yards. How many 1-inch strips can be cut from the line? Answers:a 6 strips b 18 st
    14·2 answers
  • Help me please asap thank you
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!