4. Applications of Derivatives
Differentials
Problem 4.7.77
Textbook Question
17–83. Limits Evaluate the following limits. Use l’Hôpital’s Rule when it is convenient and applicable.
lim_Θ→π/2⁻ (tan Θ)ᶜᵒˢ ᶿ
Verified step by step guidance1
Identify the limit to evaluate: lim_Θ→π/2⁻ (tan Θ)ᶜᵒˢ ᶿ.
Recognize that as Θ approaches π/2 from the left, tan Θ approaches infinity, while cos Θ approaches 0.
Rewrite the expression in a form suitable for l'Hôpital's Rule, if applicable, by expressing it as a fraction.
Differentiate the numerator and denominator separately, if using l'Hôpital's Rule is appropriate.
Evaluate the limit again after applying l'Hôpital's Rule, checking if the new limit can be determined.
Was this helpful?
