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

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The discussion focuses on finding limits without using L'Hôpital's rule, as it is not part of the syllabus. Participants share strategies for converting indeterminate forms, particularly focusing on transforming expressions into forms like 1∞. They emphasize the importance of showing initial attempts to receive help and discuss the use of logarithmic properties and trigonometric identities to simplify the limits. One user successfully solves two of the three limits discussed and plans to seek further clarification from a teacher regarding the first limit. The conversation highlights the collaborative effort to understand limit-solving techniques outside of standard rules.
  • #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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