Question

Can someone help me with calculus ab

Answer 1

given: F(x) = \[\int\limits_{1}^{x}dt/t\]

Answer 2

a. Determine the open interval over which F(x) represents an antiderivative of f(x) = 1/x

Answer 3

b. Find the x-intercept of F(x)

Answer 4

I don't think b is a problem but how do you do part a?

Answer 5

a) i think the open interval is (1, oo ) or (1, infinity )

Answer 6

Ok this is antiderivative but how do I know the interval

Answer 7

the antiderivative is ln t , not t

Answer 8

x can vary from 1 to some positive number , so 1 to infinity

Answer 9

Wait but the antiderivative is x-1 right?

Answer 10

it is not 1 to infinity

Answer 11

oh wait, i guess it should be ( 1 , x ) , where x>1

Answer 12

Wait perl said the antiderivative is lnt?

Answer 13

yes, because F(x) = ln (x) - ln (1) = ln (x) - 0 = ln(x)

Answer 14

Ya I think that's right because F(x) is the antiderivative of 1/x.

Answer 15

the antiderivative of 1/t is ln | t | , yes

Answer 16

You all helped. Thanks a lot :]

Answer 17

and and F(x) = ln (x) = 0 , when x = 1 , so you are right

Answer 18

to find x intercept you solve F(x) = 0 , i believe

Answer 19

Yup I got it

Answer 20

the answer to (a) is \[(0,\infty)\]

Answer 21

@Zarkon
i thought you said (0,infinity) is not the answer to a) ?

Answer 22

1/t is continuous on (0,infiniity)

Answer 23

when did I say that

Answer 24

You said it's not 1 to infinity

Answer 25

scroll up, you said 'it is not 1 to infinity '

Answer 26

It's 0 to infinity

Answer 27

But why 0 and not 1...

Answer 28

no , it is 1 to x where x is any real number greater than 1

Answer 29

because 1/t is continuous on (0,infiniity)

Answer 30

infinity is not a number, technically

Answer 31

Ya but we can still write infinity for intervals can't we

Answer 32

(0,infinity ) creates an improper integral

Answer 33

thus the open parentheses and not closed

Answer 34

It says "open interval"

Answer 35

\[(0,\infty)\] is an open interval

Answer 36

You got this by knowing that the domain of lnx is (0, infinity) right

Answer 37

http://mathworld.wolfram.com/FundamentalTheoremsofCalculus.html

Answer 38

http://mathworld.wolfram.com/SecondFundamentalTheoremofCalculus.html

Answer 39

Ya I remember learning this

Answer 40

here your f(t)=1/t

it is continuous on (0,infinity)

1 is in the interval (0,infinity)

therefore if \[F(x)=\int\limits_{1}^{x}\frac{1}{t}dt\]

then \[F'(x)=f(x)\]

on (0,infinity)

Answer 41

Ok thank you