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salantis [7]
3 years ago
5

I WILL GIVE BRAINLIEST AND 100 POINTS!! NEED NUMBER 11 (ignore all writing

Mathematics
1 answer:
madreJ [45]3 years ago
4 0
-2-(-12) the total is 10
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Consider functions of the form f(x)=a^x for various values of a. In particular, choose a sequence of values of a that converges
sleet_krkn [62]

Answer:

A. As "a"⇒e, the function f(x)=aˣ tends to be its derivative.

Step-by-step explanation:

A. To show the stretched relation between the fact that "a"⇒e and the derivatives of the function, let´s differentiate f(x) without a value for "a" (leaving it as a constant):

f(x)=a^{x}\\ f'(x)=a^xln(a)

The process will help us to understand what is happening, at first we rewrite the function:

f(x)=a^x\\ f(x)=e^{ln(a^x)}\\ f(x)=e^{xln(a)}\\

And then, we use the chain rule to differentiate:

f'(x)=e^{xln(a)}ln(a)\\ f'(x)=a^xln(a)

Notice the only difference between f(x) and its derivative is the new factor ln(a). But we know  that ln(e)=1, this tell us that as "a"⇒e, ln(a)⇒1 (because ln(x) is a continuous function in (0,∞) ) and as a consequence f'(x)⇒f(x).

In the graph that is attached it´s shown that the functions follows this inequality (the segmented lines are the derivatives):

if a<e<b, then aˣln(a) < aˣ < eˣ < bˣ < bˣln(b)  (and below we explain why this happen)

Considering that ln(a) is a growing function and ln(e)=1, we have:

if a<e<b, then ln(a)< 1 <ln(b)

if a<e, then aˣln(a)<aˣ

if e<b, then bˣ<bˣln(b)

And because eˣ is defined to be the same as its derivative, the cases above results in the following

if a<e<b, then aˣ < eˣ < bˣ (because this function is also a growing function as "a" and "b" gets closer to e)

if a<e, then aˣln(a)<aˣ<eˣ ( f'(x)<f(x) )

if e<b, then eˣ<bˣ<bˣln(b) ( f(x)<f'(x) )

but as "a"⇒e, the difference between f(x) and f'(x) begin to decrease until it gets zero (when a=e)

3 0
3 years ago
Ona took a random sample of 20 soccer teams across Europe. She tracked the average number of goals
anygoal [31]

The predicted number of wins for a team that averages 1.5 goals per game will be 17 according to the regression model.

From the table given, the linear regression model for the data can be expressed as :

  • y = 14.02x - 3.64 ; where ;
  • y = Predicted number of wins ;
  • x = average number of goals per match ;
  • slope = 14.02 ;
  • Intercept = - 3.64

<u>The Number of wins for a team which averages 1.5 goals per match can be calculated thus</u> :

Average goals per match, x = 1.5

Substitute x = 1.5 into the equation :

y = 14.02(1.5) - 3.64

y = 17.39

y = 17 (nearest whole number)

Learn more :brainly.com/question/18405415

8 0
2 years ago
Some queen bumblebees weigh up to 0.850.850, point, 85 grams.
LUCKY_DIMON [66]

Answer:

1g

Step-by-step explanation:

4 0
3 years ago
What is the value of C-F​
photoshop1234 [79]

Answer:

The sweat chloride reference value is less than 30 mmol/L. A value of more than 60 mmol/L of chloride in the sweat is consistent with a diagnosis of cystic fibrosis. The values of 30-60 mEq/L may represent heterozygous carriers, these carriers cannot be accurately identified with a sweat chloride test.

4 0
3 years ago
What are the x- and y-intercepts for a line with one point at (2,1) and another at (6,3)?​
OverLord2011 [107]

Answer:

x - intercept = 0 and y - intercept = 0

Step-by-step explanation:

Using the two point slope intercept form, the formula is;

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

We are given the intercepts to be at

(2,1) and (6,3).

So, x1 = 2 and x2 = 6,while y1 = 1 and y2 = 3

Plugging into the equation, we have;

(y - 1)/(x - 2) = (3 - 1)/(6 - 2)

(y - 1)/(x - 2) = 2/4

(y - 1)/(x - 2) = 1/2

Cross multiply to get;

2(y - 1) = x - 2

2y - 2 = x - 2

2y = x

Now, the x intercept will occur at y = 0.

Thus,

2(0) = x

x = 0

Also, the y intercept occurs when x = 0.

So, 2y = 0

y = 0

x - intercept occurs at (0,0) and y - intercept occurs at (0,0)

5 0
3 years ago
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