Limit Definition of Derivative

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SUMMARY

The limit definition of a derivative is expressed as [f(x+h)-f(x)]/h as h approaches zero, which equals f'(x). In the context of the discussion, the limit is confirmed to be equal to g'(\pi), where g'(\pi) is evaluated using the secant function, specifically sec(\pi) = -1. The calculation shows that subtracting -1 results in a positive 1, affirming the correctness of the limit definition in this scenario.

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  • Understanding of calculus concepts, specifically derivatives.
  • Familiarity with limit notation and evaluation.
  • Knowledge of trigonometric functions, particularly secant.
  • Ability to interpret mathematical expressions and equations.
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  • Learn about the properties and applications of the secant function.
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Qube
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Homework Statement




http://i.minus.com/jbicgHafqNzcvn.png

Homework Equations



The limit definition of a derivative:

[f(x+h)-f(x)]/h as h approaches zero is f'(x)

The Attempt at a Solution



I'm just not understanding the wording of the question. The limit given in the question is indeed equal to g'(x) since it's set up properly and indeed sec(pi) is -1 and subtracting -1 makes it a positive 1.
 
Last edited by a moderator:
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Qube said:

Homework Statement




http://i.minus.com/jbicgHafqNzcvn.png

Homework Equations



The limit definition of a derivative:

[f(x+h)-f(x)]/h as h approaches zero is f'(x)

The Attempt at a Solution



I'm just not understanding the wording of the question. The limit given in the question is indeed equal to g'(x)

You mean ##g'(\pi)##

since it's set up properly and indeed sec(pi) is -1 and subtracting -1 makes it a positive 1.

So I guess you would mark it True.
 
Last edited by a moderator:

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