- #1
UrbanXrisis
- 1,196
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[tex]lim_{h->0}\frac{ln(2+h)-ln2}{h}[/tex]
so I need to get rid of the 'h' on the denominator, but how can I do that?
so I need to get rid of the 'h' on the denominator, but how can I do that?
just to play devils advocate ...dextercioby said:Folklore says that Leibniz discovered diff.calculus while playing with tangents to curves...
Daniel.
UrbanXrisis said:how do I actually solve the problem?
UrbanXrisis said:okay,I understand all that you have said. f(x) is ln(x).
how do I actually solve the problem?
dextercioby said:What do you mean...?It's already solved with the derivative's definition.
SpaceTiger said:If this is like the structure of my old calc class, he may not have covered derivatives yet.
UrbanXrisis said:I've learned derivatives, I think I just forget the definition of a derivative and how to solve the definition, it was a while back and my class is doing some basic review
SpaceTiger said:Well, if you're allowed to solve this problem by invoking the derivative of a logarithm, just do that. Otherwise:
[tex]\frac{\ln (2+h) - \ln(2)}{h} = \ln \left[\left( 1 +\frac{h}{2}\right)^{\frac{1}{h}}\right][/tex]
Explain to me how this is true so that I can be sure that you're following.
[tex]\frac{\ln (2+h) - \ln(2)}{h} = \frac{\ln(\frac{2+h}{h})}{h}= \ln \left[\left( 1 +\frac{h}{2}\right)^{\frac{1}{h}}\right][/tex]
Quite right but i was referring to the method that is used, it was first proposed before calculus by Fermat to find the slope of the line tangent to a point, although it's not the same notation as in calculus here's http://math.kennesaw.edu/~jdoto/13.pdf (goto Fermat's method) .dextercioby said:Folklore says that Leibniz discovered diff.calculus while playing with tangents to curves...
Daniel.
The 'h' on the denominator refers to the variable used in the denominator of a mathematical expression.
In certain mathematical operations, having the variable 'h' in the denominator can make it difficult to solve the equation or find the limit. Removing the 'h' can simplify the problem and make it easier to solve.
The process of removing the 'h' on the denominator depends on the specific mathematical expression or problem. It may involve factoring, simplifying, or using algebraic manipulation to eliminate the 'h' term.
Yes, there are certain situations where it may not be possible or appropriate to remove the 'h' on the denominator. This could be due to the structure of the equation or the mathematical properties involved.
Yes, removing the 'h' on the denominator can change the solution to a problem. It is important to carefully consider the steps taken to remove the 'h' and ensure that the solution is still accurate and valid.