Limit Solving Strategies for Non-L'Hôpital's Rule Problems

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Homework Help Overview

The discussion revolves around finding limits of various functions without using L'Hôpital's rule, as it is not permitted in the participants' coursework. The original poster expresses difficulty in solving three specific limits among a larger set.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss converting expressions into indeterminate forms, such as 1∞ and 0/0. There are attempts to express trigonometric functions in terms of logarithms and to explore different bases for logarithms. Some participants question the original poster's attempts and encourage showing work to facilitate assistance.

Discussion Status

There is ongoing exploration of various approaches to the limits, with some participants providing hints and suggestions for reworking the problems. The discussion includes multiple interpretations and attempts to clarify the setup of the limits. No consensus has been reached, and the original poster is encouraged to seek further guidance from a teacher.

Contextual Notes

Participants note that certain standard limits and derivative rules are not covered in the original poster's coursework, which may limit their ability to solve the problems effectively. The original poster acknowledges confusion regarding the base of logarithms used in their attempts.

  • #31
shalikadm said:
We have not such rule in Limits but in differential calculus we were taught,
y=f(x)g(x)
\frac{dy}{dx}=g(x)f'(x)+f(x)g'(x)

Exactly. Use this rule to differentiate y*sec(y), that's the answer you are looking for!
 
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  • #32
what about the [3] one?
 
  • #33
shalikadm said:
what about the [3] one?

Convert \frac{1}{\sqrt{2}} into cos(\frac{\pi}{4}), and apply the formula that changes the difference of two trigonometric terms into their product. In the denominator, after writing cot in terms of cos and sin, try getting a single trigonometric ratio and simplify.
 
  • #34
thanks Infinitum and Pranav-Arora...Successfully solved the 2nd and 3rd limits..I'm going to ask about 1st one from a teacher...thanks for the help !
 

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