MHB Solving a Logarithmic Curve: Tangent Lines & Approximations

[fuzz95]

guys I need loads of help for this question(s)?

what do i even do ?!?

Sketch the curve y = lnx and find the tangent line to this curve at the point where the curve crosses the x-axis. Deduce that, for small delta,
ln(1 + δ) ≈ δ .

- I know what the y = Inx curve looks like but what do i do after that?? how do i find my tangent line, etc ?

Use the approximation from the previous part to deduce that
p = p(h) ≈ Ae^-0.004h/30 .

THanks

 

[Ackbach]

Re: y=Inx

To find the equation of a line, you need to know either two points on the line, or a slope and a point. Which do you think you'll have in this case?

 

[fuzz95]

Re: y=Inx

To find the equation of a line, you need to know either two points on the line, or a slope and a point. Which do you think you'll have in this case?

nupe??
is the slope just 1 ?
how do i know two points on the line?

 

[MarkFL]

Re: y=Inx

nupe??...

I don't know what that means. :D

is the slope just 1 ?
how do i know two points on the line?

How did you determine the slope of the tangent line is 1? And, if you know a point on the line and its slope, how can you determine the equation of the line?

 

[Deveno]

Psst...fuzz95, the derivative of a function is also known as the ____ of the function at that point.

 

[fuzz95]

Re: y=Inx

I don't know what that means. :D
How did you determine the slope of the tangent line is 1? And, if you know a point on the line and its slope, how can you determine the equation of the line?

i actually have no idea what you are trying to ask me?

 

[Ackbach]

Re: y=Inx

i actually have no idea what you are trying to ask me?

Let's go back a little and discuss philosophy just a bit. MHB is a site where people can ask math questions and get a very specific kind of help: unsticking. MHB does not generally offer complete solutions to every problem posted. Nor are we a homework service. Users such as yourself, who are asking math questions, are expected to do the heavy lifting: tell us where you're stuck, exactly, and what you're not understanding; then we help you get unstuck. This maximizes your learning, because you'll own the solution for yourself.

That said, let's go back in another way, and check some basic understanding. Please answer the following questions:

1. What is the equation of a line (any line, not just a tangent line or a secant line)?

2. What is the slope of a line (again, any line)?

3. How do you compute the slope of a line (again, any line)?

4. Suppose I were to give you the slope of a line, and a point on the line. How would you find the equation of the line?

5. Suppose I were to give you two points on a line. How would you find the equation of the line?

 

[fuzz95]

Re: y=Inx

Let's go back a little and discuss philosophy just a bit. MHB is a site where people can ask math questions and get a very specific kind of help: unsticking. MHB does not generally offer complete solutions to every problem posted. Nor are we a homework service. Users such as yourself, who are asking math questions, are expected to do the heavy lifting: tell us where you're stuck, exactly, and what you're not understanding; then we help you get unstuck. This maximizes your learning, because you'll own the solution for yourself.

That said, let's go back in another way, and check some basic understanding. Please answer the following questions:

1. What is the equation of a line (any line, not just a tangent line or a secant line)?

2. What is the slope of a line (again, any line)?

3. How do you compute the slope of a line (again, any line)?

4. Suppose I were to give you the slope of a line, and a point on the line. How would you find the equation of the line?

5. Suppose I were to give you two points on a line. How would you find the equation of the line?

okay so i get that when x= 1, ln(x) crosses the x axis
Therefore ln(1) = 0 right?
Therefore ln(1+d) = d
- for d small enough (since the function slowly increases from zero as x increases from 1)
so that's my understanding of the question, etc? but from that i don't get how do find the second part of the question?

 

[Opalg]

Re: y=Inx

okay so i get that when x= 1, ln(x) crosses the x axis
Therefore ln(1) = 0 right?
Therefore ln(1+d) = d
- for d small enough (since the function slowly increases from zero as x increases from 1)
so that's my understanding of the question, etc? but from that i don't get how do find the second part of the question?

You put this question in the calculus section of the forum, so presumably you know something about calculus. Can you think of anything that calculus tells you about how to make that statement in green a bit more precise? In other words, instead of just saying that the function "slowly increases", can you use calculus to find the exact rate of increase of the function $\ln x$ when $x=1$?

 

[Deveno]

Re: y=Inx

okay so i get that when x= 1, ln(x) crosses the x axis
Therefore ln(1) = 0 right?

This is correct.

Therefore ln(1+d) = d
- for d small enough (since the function slowly increases from zero as x increases from 1)

How d'ya figure? This does not seem a forgone conclusion.

so that's my understanding of the question, etc? but from that i don't get how do find the second part of the question?

Question: what is a tangent line, and how do we find their equations? Do you know this? If you have no idea, then everything else you're doing is just guesswork.