The solution is Option C.
The equation f'( 2 ) ≤ 0 is true
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
[tex]f ( x ) = \lim_{n \to \infty} [ \frac{( n^{n} ( x + n ) ( x + \frac{n}{2} ) ....( x + \frac{n}{n} )}{n! (x^{2}+n^{2}) ( x^{2} + \frac{n^{2}}{4} ) ....( x^{2} +\frac{n^{2}}{n^{2} } ) } ]^{\frac{x}{n} }[/tex]
Taking logarithm on both sides of the equation , we get
[tex]ln f ( x ) = \lim_{n \to \infty} \frac{x}{n} [\sum _{r=1}^nln\frac{1}{r/n} + \sum _{r=1}^nln\frac{(x + \frac{1}{r/n} )}{(x^{2} + (\frac{1}{r/n})^{2} ) }[/tex]
On simplifying the derivatives of the equation , we get
[tex]ln f ( x ) = x [\int\limits^1_0 {ln ( 1/t )} \, dt + \int\limits^1_0 {ln \frac{( x+1/t )}{(x^{2} + 1/t^{2} ) } } \, dt][/tex]
Now , substituting the limits in the equation , we get
[tex]ln f ( x ) = x [ \int\limits^1_0 {( - ln t+ ln (tx+1)-lnt-ln(t^{2} x^{2}+1)+lnt^{2}] } \, dt[/tex]
Substitute the value of tx = z in the equation , we get
[tex]ln f ( x ) = \int\limits^1_0 {ln\frac{(1+z)}{1+z^{2} } } \, dz[/tex]
Taking exponential on both sides of the equation , we get
[tex]f ( x ) = e^{\int\limits^x_0 {{ln\frac{(1+z)}{1+z^{2} } } \, dz} \, }[/tex]
Differentiating with respect to x , we get
[tex]\frac{f' (x ) }{f ( x ) } = ln\frac{1+x}{1+x^{2} }[/tex]
Now , on further simplification of the equation , we get
f ( x ) > 0 for x > 0
And , f' ( x ) > 0
[tex]ln\frac{1+x}{1+x^{2} } > 0[/tex]
And ,
x > x²
0 < x < 1
Therefore , f ( x ) is increasing ∀ x ∈ ( 0 , 1 )
Hence , the equation f' ( 2 ) ≤ 0 is true
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Explanation:
[tex] \rm f(x) = \lim \limits_{n \to \infty } \left( \dfrac{ \displaystyle \rm \prod \limits_{r = 1}^n \left(1 + \dfrac{rx}n \right ) }{\displaystyle \rm\prod \limits_{r = 1}^n \left(1 + \bigg(\dfrac{rx}n \bigg)^{2}\right )} \right)^{ \dfrac{x}{n} }[/tex]
[tex] \large \rm = {e}^{ x \int \limits_{0}^{1} ln(1 + xy)dy - ln(1 + (xy {)}^{2} ) dy }[/tex]
[tex]\rm f'(x)=f(x) \ln \bigg( \dfrac{1 + x}{1 + {x}^{2} } \bigg)[/tex]
[tex]\rm For \: x \in(0,1) \: it \: i s \: increasing \: function[/tex]
[tex]\rm f'(2) = f(2) \ln( \frac{3}{5} ) < 0[/tex]
[tex]\rm \dfrac{f'(3)}{f(3)} =ln \bigg( \dfrac{2}{5} \bigg), \dfrac{f'(2)}{f(2)} = ln \bigg( \dfrac{3}5 \bigg) [/tex]
Calculate the area of the shaded area !!
EZ FREE POINTS!!
Answer:
20 sq units
Step-by-step explanation:
Answer:
20 sq units
Hope it helps :)
X^2(x+5)
Help me PLS
Answer: x^3+5x^2
Step-by-step explanation:
PLEASE HELP! this is a 4 part problem but here is the last part :)!!!
2/14 as a decimal (please explain)
Answer:
Hi! The answer to your question is 0.142857. (Convert the fraction to a decimal by dividing the numerator by the denominator)
Step-by-step explanation:
☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
A student incorrectly says the volume of the regular hexagonal prism, to the nearest cubic centimeter, is 1,619 cm3. What is the correct volume? What error did the student most likely make?
The volume of the regular hexagonal prism is ___ cm3.
Answer:
17.5
Step-by-step explanation:
Steve reaches into a bag with 5 marbles 3 yellow marbles and 2 green marbles and randomly selects one the he puts the marble back and sam reaches into the same bag and randomly selects a marble is this independent or dependent
Answer:
Independent
Step-by-step explanation:
The reliance of an event on the outcine of another event gives rise to a dependent event. For any two or more event, whereby the outcome of event A has no effect on the possible outcome of event B, then such scenario is termed as being Independent. In the scenario described above, the outcome oof Sam's pick does not depend on the outcine of Steve's pick. This is because, once Steve makes his selection, the marble is returned into the box before Sam makes his own selection.Therefore, no matter the color of marble picked by Steven, it will have no bearing on the outcome of Sam's pick.
Sketch the graph of the following equations: y=x+5, y=-(x+5), and y = |x+5|
The graph of functions y=x+5, y=-(x+5), and y = |x+5| are shown in figure.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Equations are,
y = x + 5
y = - (x + 5)
y = |x + 5|
Since, All equations shows equation of line.
Hence, We can draw all the equations as shown in figure.
y = x + 5
Slope = 1
y - intercept = 5
y = - x - 5
Slope = - 1
y - intercept = - 5
Thus, The graph of functions y=x+5, y=-(x+5), and y = |x+5| are shown in figure.
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i need help with this
Answer:
<FNM = 73
Step-by-step explanation:
we are given
GNF = 60
MNL = 47
60+47=107
107-180=73
Ashleys Shoe Store buys shoes for $35 and then sells them for
$85.
What is the percent of increase on the price of the shoes?
Round to the nearest whole number
What's the common difference of the sequence -5, -2, 1, 4, 7, ...?
A) d= -5
B) d= 2
C) d=-3
D) d= 3
Answer:
The answer is D) d=3!!!!!
find the value of each variable
Answer:
x = 16 y= 16√3
Step-by-step explanation:
we know that a angle is 60 degrees. Thanks to this information we can say that x is half the hypothenuse, so is value is 16.
y can be express as √3/2 x 32 = 16√3
PLEAS EHELP ILL GIVE BRAINLIEST
PLEASE SHOW ALL WORK AND BE SPECIFIC
Answer:
Where is the question? You didn't post it.
COMPOSITE FIGURES!!! can you please help
What is the sum of (3x – 6) + (2x + 5)?
Answer: 5x - 1
Step-by-step explanation: 3x + 2x = 5x and -6 + 5 = -1, so 5x - 1.
Answer:
The sum of (3x – 6) + (2x + 5) is 5x - 1
Step-by-step explanation:
(3x - 6) + (2x + 5)
3x - 6 + 2x + 5
3x + 2x - 6 + 5
5x - 1
Thus, The sum of (3x – 6) + (2x + 5) is 5x - 1
-TheUnknownScientist
HELPPPPPPP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answer:
answer is 9
Step-by-step explanation:
1st method: Proportion
15/100 = n/60
cross-multiply to get:
100n = 900
n = 900/100
n = 9
2nd method: Convert % to Decimal and Multiply
.15 × 60 = 9
Given: BD bisects AE, A = E
Prove: ABC EDC
(No links)
Answer:
All sides are equal better explenation bellow
Step-by-step explanation:
It's a mirror flip of a ABC triangle
Yet you can say AB Is = to DE
And since most likely it's a 60° triangle all the angles are 60°
All triangles have 180°
Which means AB =BC
BC= AC
BC =CD
DE= CD
CE=DE
Which means all the sides are equal
Can someone help me with this one too please
Answer:
1) f - 2
2) 45 + b
3) s - 82
4) 52c
5) t/5
Answer:
1) f-2
2) 45+b
3) s-82
4)52c
5)t/5
Area of Composite Figures
-1.5 in.
10 in.
A
6 in
4 in.
1.5 in.
17 inches squared
0.40 inches squared
52 inches squared
0 61 inches squared
Answer:
Step-by-step explanation:
What is the surface area of the rectangular prism that can be formed using this net?
Answer:
S = 2(lw + lh + wh)Step-by-step explanation:
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Joan paid $47.98 for a jacket. If the tax rate is 8.25%, what was the cost of the jacket before tax?
Answer:
$44.021
Step-by-step explanation:
$47.98 - 8.25% = $44.021
Priscilla received 240 votes in the election for student council president. That was 60% of the students who voted in the election. How many students voted in the election? *
Answer:
400 students voted in the election
Step-by-step explanation:
Given:
Total number of votes received by Priscilla = 240
This was 60% of the students who voted in the election.
To find: Total number of students who voted in the election
Solution:
Total number of votes received by Priscilla = 60% of Total number of students who voted in the election
240 = 60% of Total number of students who voted in the election
240 = [tex]\frac{60}{100}[/tex] × Total number of students who voted in the election
So,
Total number of students who voted in the election [tex]=\frac{240(100)}{60}=400[/tex]
what is the same as 8/9?
Answer:
8×1/9
Step-by-step explanation:
It is same as 8/9 because 8×1=8
What value of x will make the equation below true?
14−(x+7)=3
Root5 /2 root5 -1
can be written in the form
a+rootb /c
where a, b and c are integers.
Find the values of a, b and c when the resulting fraction
is written in its simplest form.
Answer:
10, 5, 19
Step-by-step explanation:
Recall that
[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
So we can multiply the fraction by
[tex] \frac{2 \sqrt{5} + 1 }{2 \sqrt{5} + 1 } [/tex]
And get
[tex] \frac{ \sqrt{5} }{2 \sqrt{5} - 1} \times \frac{2 \sqrt{5} + 1 }{2 \sqrt{5} + 1 } = \frac{10 + \sqrt{5} }{20 - 1} = \frac{10 + \sqrt{5} }{19} [/tex]
Find the measure of the sixth interior angle of a hexagon if the measure
of the other five interior angles are 80°, 90°, 130°, 130°, and 150°. (Show
all work)
Answer:
140°
Step-by-step explanation:
The sum of interior angles of a n-agon is (n - 2) * 180°
a hexagon should have the sum of angles equal to
4 * 180° = 720°
Now we know that the other five angles have total measure
80° + 90° + 130° + 130° + 150° = 580°
So the sixth one has to be:
720° - 580° = 140°
Answer:140°
Step-by-step explanation: required equation : 180*(n-2)
since it is a hexagon, the sum of all interior angles=180*(6-2)
=180*4 =720°
now the measure of 6th angle=720 -(80+90+130+130+150)
= 720 -580
= 140
Can some one help? PLEASE!!!!!!!!
Troy and two of his friends help troy's dad do yard work. After his dad paid $35 for gas, the boys made 128. How much did each child make?
It wants me to find m∠2 from this
Answer:
Alternate interior angles have the same measure. As we know that 'angle 1 ' and 50° are alternate interior angles hence they must be equal. Also we now that sum of all the angles of a triangle is equal to 180°. Hence, m∠2=15°
Step-by-step explanation:
Answer:
90°
Step-by-step explanation:
This is a kite.
The angle measures of the diagonals (the lines in the middle) are always going to be 90° if they looks like this without any other measures. This goes for all other quadrilaterals as well.
m∠2=90°
Hope I helped.
A scale drawing of a dance floor is shown. What is the area of the actual dance floor? 22 cmon the top and bottom and 14 cm on the sides 5 cm equals 8 feet
Answer:
The area of the dance floor will be 788.48ft²
Step-by-step explanation:
Since 5cm represents 8ft, it means
1cm represents 8/5ft.
The scale length is 22cm, therefore the actual length would be
22 x 8/5ft = 35.2ft
The scale breadth is 14cm, therefore the actual breadth would be
14 x 8/5ft = 22.4ft
The area of the dance floor will be
(35.2ft)(22.4ft) = 788.48ft²