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
Luba_88 [7]
3 years ago
15

Find the value of x.

Mathematics
1 answer:
brilliants [131]3 years ago
4 0

Answer:

4

Step-by-step explanation:

You might be interested in
Given f(x) = (lnx)^3 find the line tangent to f at x = 3
kirill [66]
Explanation

We must the tangent line at x = 3 of the function:

f(x)=(\ln x)^3.

The tangent line is given by:

y=m*(x-h)+k.

Where:

• m is the slope of the tangent line of f(x) at x = h,

,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.

2) By evaluating the result of f'(x) at x = h = 3, we get:

m=f^{\prime}(3)=\frac{3}{3}*(\ln3)^2=(\ln3)^2.

3) The value of k is:

k=f(3)=(\ln3)^3

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

y=(\ln3)^2*(x-3)+(\ln3)^3.

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

y=(\ln3)^2*(x-3)+(\ln3)^3

6 0
1 year ago
I need help with this question 1/2 + 2 3/4=?
enyata [817]

Answer:

3.25

Step-by-step explanation:

6 0
3 years ago
Which function is nonlinear?
lutik1710 [3]

Answer:

(-1,5), (0,4) ,(1,3) ,(3,1) is linear so dont pick it

(-4,-7), (-2,-6), (2,-4), (4,-3) is linear

you know what I'll just say it wait a minute is there like a other option

Step-by-step explanation:

U can tell by graphing them out yourself and if u see a straight line then it linear, and if you see a curved loop then it's non- linear. but I'll do it :)

4 0
3 years ago
Morgan is making accessories for the soccer team. She uses 822.48 inches of fabric on headbands for 43 players and 3 coaches. Sh
emmasim [6.3K]

Answer:

headband 17.88

Wristband 9.31

Step-by-step explanation:

headband: 822.48/(43+3)

Wristband: 400.33/43

6 0
3 years ago
Suppose that f: R --> R is a continuous function such that f(x +y) = f(x)+ f(y) for all x, yER Prove that there exists KeR su
Pachacha [2.7K]
<h2>Answer with explanation:</h2>

It is given that:

f: R → R is a continuous function such that:

f(x+y)=f(x)+f(y)------(1)  ∀  x,y ∈ R

Now, let us assume f(1)=k

Also,

  • f(0)=0

(  Since,

f(0)=f(0+0)

i.e.

f(0)=f(0)+f(0)

By using property (1)

Also,

f(0)=2f(0)

i.e.

2f(0)-f(0)=0

i.e.

f(0)=0  )

Also,

  • f(2)=f(1+1)

i.e.

f(2)=f(1)+f(1)         ( By using property (1) )

i.e.

f(2)=2f(1)

i.e.

f(2)=2k

  • Similarly for any m ∈ N

f(m)=f(1+1+1+...+1)

i.e.

f(m)=f(1)+f(1)+f(1)+.......+f(1) (m times)

i.e.

f(m)=mf(1)

i.e.

f(m)=mk

Now,

f(1)=f(\dfrac{1}{n}+\dfrac{1}{n}+.......+\dfrac{1}{n})=f(\dfrac{1}{n})+f(\dfrac{1}{n})+....+f(\dfrac{1}{n})\\\\\\i.e.\\\\\\f(\dfrac{1}{n}+\dfrac{1}{n}+.......+\dfrac{1}{n})=nf(\dfrac{1}{n})=f(1)=k\\\\\\i.e.\\\\\\f(\dfrac{1}{n})=k\cdot \dfrac{1}{n}

Also,

  • when x∈ Q

i.e.  x=\dfrac{p}{q}

Then,

f(\dfrac{p}{q})=f(\dfrac{1}{q})+f(\dfrac{1}{q})+.....+f(\dfrac{1}{q})=pf(\dfrac{1}{q})\\\\i.e.\\\\f(\dfrac{p}{q})=p\dfrac{k}{q}\\\\i.e.\\\\f(\dfrac{p}{q})=k\dfrac{p}{q}\\\\i.e.\\\\f(x)=kx\ for\ all\ x\ belongs\ to\ Q

(

Now, as we know that:

Q is dense in R.

so Э x∈ Q' such that Э a seq belonging to Q such that:

\to x )

Now, we know that: Q'=R

This means that:

Э α ∈ R

such that Э sequence a_n such that:

a_n\ belongs\ to\ Q

and

a_n\to \alpha

f(a_n)=ka_n

( since a_n belongs to Q )

Let f is continuous at x=α

This means that:

f(a_n)\to f(\alpha)\\\\i.e.\\\\k\cdot a_n\to f(\alpha)\\\\Also\\\\k\cdot a_n\to k\alpha

This means that:

f(\alpha)=k\alpha

                       This means that:

                    f(x)=kx for every x∈ R

4 0
3 years ago
Other questions:
  • Can you please help? I know the one I chose is correct.
    6·2 answers
  • Identify the meaning of the variables in the point slope from of the a lines
    10·1 answer
  • Please help answer question above.
    6·1 answer
  • PLZ HELP! QUICK! WILL MARK BRAINLIEST!!! 20 POINTS!!! A portion of the Quadratic Formula proof is shown. Fill in the missing sta
    5·1 answer
  • Which one is greater -1.7 or -1
    10·1 answer
  • What is 73 square inches. What is the paper's area in square centimeters?
    6·1 answer
  • Prove. sin³A-cos³A/sinA-cosA = 1+sinAcosA​
    15·1 answer
  • Howe do I solve it 5=n/5+8
    11·1 answer
  • Choose the correct converse.
    5·1 answer
  • 14 1/2 - 2 1/3 what is the answer to this equation?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!