How to find the limit of a complicated function using L'Hopital's rule?

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Homework Help Overview

The discussion revolves around finding the limit of a vector-valued function as t approaches zero, specifically involving terms with sine, exponential, and polynomial components.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the limit of the sine function divided by a linear term, questioning the interpretation of the limit and the reasoning behind the given answer. Some mention L'Hôpital's rule as a potential method to resolve the indeterminate form.

Discussion Status

The discussion includes attempts to clarify the limit of sin(t)/(2t) as t approaches zero, with some participants recalling standard limits and others expressing confusion about the derivation of the answer. There is acknowledgment of L'Hôpital's rule as a relevant technique.

Contextual Notes

Participants note the indeterminate form 0/0 and the need for further exploration of the limit's components. There is a reference to the standard limit of sin(t)/t as t approaches zero, which may influence the understanding of the problem.

don23
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can someone help me out with a simple calc question?

we are asked to find the limit of a function as t approaches zero. the function is:

(sint/2t)i + (e^2t)j + (t^2/e^t)k

why is the answer not just j?

the answer given is 1/2i + j, but I have no idea how that first term came about.

help!
 
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sin(t)/(2t) as t->0 is one of those indeterminate 0/0 forms, it's not 0 as you seemed to hope. You should know the limit of sin(t)/t as t->0, it's a pretty standard one (or you can use l'hopital's rule).
 
don23 said:
can someone help me out with a simple calc question?

we are asked to find the limit of a function as t approaches zero. the function is:

(sint/2t)i + (e^2t)j + (t^2/e^t)k

why is the answer not just j?

the answer given is 1/2i + j, but I have no idea how that first term came about.

help!
\lim_{t{\to}0}\frac{\sin{t}}{t}=1

edit: i can't remember the diravation at the moment
 
Last edited:
thank you

thank you:) it's been a while...i forgot about l'hopital's rule. thanks again
 

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