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

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SUMMARY

This discussion focuses on solving limit problems without using L'Hôpital's Rule, as it is not part of the syllabus. Participants explore various strategies, including converting expressions into indeterminate forms like 1∞ and utilizing logarithmic properties. Key techniques discussed include expressing trigonometric functions in terms of sine and cosine, and applying the definition of derivatives in limit form. The conversation emphasizes the importance of showing attempts to receive assistance and understanding foundational limits.

PREREQUISITES
  • Understanding of limits and indeterminate forms in calculus
  • Familiarity with trigonometric identities and properties
  • Knowledge of logarithmic functions and their properties
  • Basic differentiation techniques, including the product rule
NEXT STEPS
  • Study the properties of logarithms and their applications in limits
  • Learn how to convert trigonometric expressions into different forms
  • Explore the definition of derivatives and their use in limit problems
  • Practice solving limits using various techniques without L'Hôpital's Rule
USEFUL FOR

Students studying calculus, particularly those focusing on limits and differentiation, as well as educators seeking to enhance their teaching methods in these areas.

  • #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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