Question

last calc problem if someone can please check!!

Answer 1

f(x)=x^10

Answer 2

@adamaero can you please please check this last one??

Answer 3

Do you have some idea?

Answer 4

what do you think?

Answer 5

i just graph them and see which one grows the fastest right? @adamaero

Answer 6

yep

Answer 7

What, did you think you had to take a limit?

Answer 8

noo i graphed and got B(:

Answer 9

so
ln(100^10) > 10^100
?

Answer 10

noo oops

Answer 11

let me graph them again

Answer 12

F(x)=x^10 if this isnt rght then im not graphing it right

Answer 13

the logarithm is really a slow function
try evaluating big number and see in comparison to exponential function
and power function (polynomial )

Answer 14

then the same way you can compare x^10 with 10^x

Answer 15

my final answer - A

Answer 16

that's incorrect

Answer 17

compare
the following values:
\[100^{10} \text{ and } 10^{100}\]

Answer 18

\[100=10^2 \\ (10^2)^{10}=?\]

Answer 19

1*10^20

Answer 20

so which is larger?
\[10^{20} \text{ or } 10^{100} ?\]

Answer 21

10^100

Answer 22

then we can say that the exponetial \[f(x)=10^x\] is greater than the power function
\[f(x)=x^{10}\]

Answer 23

yeah correct
the exponential function is very fast

Answer 24

it just blows to bigger values really fast

Answer 25

http://www.wolframalpha.com/input/?i=plot++f%28x%29%3D10%5Ex+and+g%28x%29%3Dx%5E%2810%29%2C+x%3D5...15
I think this graph shows it pretty well too
if you couldn't get your calculator to show it well enough

Answer 26

The larger x domain I chose the graph of y=x^(10) didn't even become visible

Answer 27

that is because that function was getting to infinity much slower

Answer 28

a) f(x) = x^10
f'(x) = 10 * x^9

b) f(x) = ln(x^10) = 10ln(x)
f'(x) = 10 / x

c) f(x) = 10^x
f'(x) = ln(10) * 10^x

As x-->infinity, (b) goes to zero but (a) and (c) both approach infinity.
Which one, (a) or (c), increases at a faster rate?
Try x = 100:
a) f'(100) = 10 * 100^9 = 10 * (10^2)^9 = 10 * 10^18 = 10^19 (1 followed by 19 zeros).
c) f'(100) = ln(10) * 10^100 (approx. 1 followed by 100 zeros).

(c) increases at a faster rate as x becomes very large.