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asimon2008
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Homework Statement
48. Lim (cscx- cotx)
x-0
52. lim (xe^1/x -x)
x-∞
Indeterminate forms and L'Hospital's Rule
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SUMMARY
The discussion focuses on evaluating two limits involving indeterminate forms using L'Hospital's Rule. The first limit, Lim (cscx - cotx) as x approaches 0, requires the application of trigonometric identities and L'Hospital's Rule to resolve the indeterminate form. The second limit, lim (xe^(1/x) - x) as x approaches negative infinity, also necessitates L'Hospital's Rule to simplify the expression and find the limit accurately.
PREREQUISITES- Understanding of L'Hospital's Rule
- Familiarity with trigonometric functions and identities
- Knowledge of limits and indeterminate forms
- Basic calculus concepts, including exponential functions
- Study the application of L'Hospital's Rule in various limit problems
- Explore trigonometric identities relevant to limit evaluations
- Learn about exponential growth and decay in calculus
- Practice solving limits involving indeterminate forms
Students studying calculus, particularly those focusing on limits and L'Hospital's Rule, as well as educators seeking to clarify these concepts for their students.
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