Solve Basic Limit Question Homework Equation

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Homework Help Overview

The discussion revolves around a limit problem involving the function f(x) and its behavior as x approaches infinity. The original poster is attempting to solve a limit question and is exploring the implications of derivatives and secant slopes in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster discusses their attempts to find a solution for the limit problem, mentioning their confidence in the first part and uncertainty in the second part. They consider using the definition of the derivative and question whether to treat the right side of the inequality as a limit. Other participants suggest examining the slopes of secants and their relationship to the slopes of tangents as x becomes large.

Discussion Status

The discussion is ongoing, with participants providing hints and prompting further exploration of the concepts involved. There is no explicit consensus, but several lines of reasoning are being examined, particularly regarding the behavior of slopes at infinity.

Contextual Notes

Participants are navigating the complexities of limits and derivatives, with some expressing difficulty in understanding the theoretical aspects being discussed. The original poster is seeking hints rather than complete solutions.

ming2194
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Homework Statement


http://u1.imgupload.co.uk/1257984000/d192_image.gif

Homework Equations


above

The Attempt at a Solution



1st part should be okay for me and my ans is e^(2c)

for the 2nd part, i have tried to use f'(x)=lim h-->infinity f(x+h)-f(x) / h and that just prove f'(x)=e but i found it maybe useless for finding c. so any hints can give me??

or may i treat right side of the inquality as lim x--> infinity f(x) - lim x--> infinity f(x-1) ?

thx:blushing:
 
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Look at the right hand side of your second part. Notice that it's

limit as x gets large of: ( f(x) - f(x-1) ) / ( x - (x-1))

If the actual derivatives of f are approaching a slope of e as x gets large, then what do you suppose is happening to slopes of secants measured way out there where x is very large?
 
LumenPlacidum said:
Look at the right hand side of your second part. Notice that it's

limit as x gets large of: ( f(x) - f(x-1) ) / ( x - (x-1))

If the actual derivatives of f are approaching a slope of e as x gets large, then what do you suppose is happening to slopes of secants measured way out there where x is very large?
soory i can't get what you mean. may be it is too theoretic for me..
 
Well, what is the form for the slope of a secant line to the graph of a function? How does that relate to the slope of the tangent line at some point?
 
delete

thx
 
Last edited:
Well done!
 

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