Question

Find f(e) if f'(x) = 10^x + 1/2x , f(1) = 2

Answer 1

+C
dont forget the constant

solve for the constant by using the information f(1) = 2

then determine f(e)

Answer 2

didnt check if the integration is correct

Answer 3

useful tool for checking integrations

http://integrals.wolfram.com/index.jsp?expr=10^x%2B1%2F%282x%29&random=false

however i wouldnt suggest relying on it too heavily

Answer 4

did I even do the antiderivative correctly..?

Answer 5

sadly, you did not. the antidervative of a^x is a^x/ln a

Answer 6

can't u take the ln of it?

Answer 7

and then product rule..

Answer 8

and for 1/2x , do you separate them as 1/2 x 1/x , then antiderivative of 1/x is ln x

Answer 9

if you take ln, then you have to apply e to keep it equivalent to to original, like this one \[10^x =e^{\ln 10^x}\]

Answer 10

you are right on an antiderivative of the second term 1/(2x)

Answer 11

ohh ok thanks. but if u ln then e, they give the same results as 10^x ln 10?

Answer 12

x ln 10 = ln10 + 1/ 10 x < if u apply e , it will be 10 + e^1/10 x which doesnt realy make sense

Answer 13

\[\ln (10^x)=x \ln 10\] and you don't have to take the derivative. it is already the derivative of the f(x)

Answer 14

ohh i get it thx.
when i do the next step
2= 10ln10 + 1/2 ln 2 +Ｃ
ln 10 + ln2 , do i combine to ln (10x2)

Answer 15

can' isolate ln

Answer 16

uh, i'm having slow refresh right now

Answer 17

i'll juz wait :)

Answer 18

i doubt you can combine them

i suggest grabbing a calcuator and calculating for C

Answer 19

my answer need to be in exact numbers

Answer 20

if thats the case, then definitely use a calculator

Answer 21

oh actually nvm, i think i know how, i've put the wrong numbers in

Answer 22

your function should be \[f(x)=\frac{ 10^x }{ \ln 10 }+\frac{ 1 }{ 2 } \ln x+C\]

Answer 23

ummm.i'm also trying to do it with xln10, but when it asks for f(e), it is weird to have e ln 10

Answer 24

why is ln in the denominator, isnt a^x is a^x ln x?

Answer 25

that is for differentiation. the antidiferrentiation causes it to be "under"

Answer 26

so x ln 10 is not the antiderivative too?

Answer 27

it is not. is is 10^x / ln 10

Answer 28

just ignore ln then e process i said earlier. it only confused you.

Answer 29

ohhh ok , yes ok, got it! thanks again sirm :D u helped alot!

Answer 30

yaw (you're always welcome) :D