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Eddi Din [679]
3 years ago
5

Joe summarised this message

Mathematics
1 answer:
Ann [662]3 years ago
4 0

Answer:

Gsmksikjvjnsn fjebbcx 50

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Whoever helps with number 5 gets brainliest answer and 10 points :)
nata0808 [166]
Count:5Sum:341Mean:68.2Median:62Mode:48, 40, 93, 62, 98
6 0
3 years ago
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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
Multiple choice: Which of the following angles, when drawn in
const2013 [10]

Answer:

Step-by-step explanation:

4

6 0
3 years ago
Common factors of 35 and 60
OLga [1]
Factors of 35: 1; 5; 7; 35
Factors of 60: 1; 2; 3; 4; 5; 6; 10; 12; 15; 20; 30; 60

<span>Greatest Common Factor GCF(35; 60) = 5</span>

4 0
3 years ago
Which graph represents the function f(x) = (x – 3)2?
Snowcat [4.5K]

Answer:

Graph 3 on Edg.

Step-by-step explanation:

6 0
3 years ago
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