L’Hôpital’s Rule is Da Bomb for Limits (Calculus Problems and Solutions)

L’Hôpital’s Rule helps us to use calculus derivatives to find limits of functions that are indeterminate forms: 0/0, ∞/∞, 0•∞, ∞^0, 1^∞, and ∞ – ∞. I work through many examples, some where algebra tricks are necessary, including using the natural logarithm function ln x. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

a.k.a. L’Hôspital’s Rule using calculus derivatives

🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2): https://www.youtube.com/watch?v=lmCjnxzIals

🔴 Calculus 1, Lesson 1.2: Exponential Functions: https://www.youtube.com/watch?v=47ZqW19AjD4

🔴 Calculus 1, Lesson 1.3: Quadratic Functions, Transformations of Functions, and Function Composition: https://www.youtube.com/watch?v=1T58CnSME4g

🔴 Calculus 1, Lesson 1.4: Logarithmic Functions (Intro to Horizontal Compressions & Inverse Functions): https://www.youtube.com/watch?v=oS-gvIoJf60

🔴 Calculus 1, Lesson 1.5: Trigonometric Functions and Inverse Trigonometric Functions: https://www.youtube.com/watch?v=UFYjlnGUenE

🔴 AP Calculus AB Exam Review: Practice Exam Problems & Solutions (Multiple Choice, No Calculator): https://www.youtube.com/watch?v=2AG_Dt3x7q0

🔴 AP Calculus AB Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=RLgUwP44V_M

🔴 AP Calculus BC Exam Review: Practice Exam (30 Question Multiple Choice, No Calculator): https://www.youtube.com/watch?v=1Q7ALcwT97A

🔴 AP Calculus BC Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=ZWisJEDP44w

🔴 Calculus 1 Exam 1 Review Problems and Solutions (Precalculus, Limits, Continuity, Derivatives): https://www.youtube.com/watch?v=UjmvUwvd7c4

🔴 Calculus 1 Course, Lecture 1: The Big Ideas (Rates & Areas, the Infinity Principle & Circular Area): https://www.youtube.com/watch?v=2V_ehJC5QUY

🔴 Calculus 1 Course Lecture Playlist: https://www.youtube.com/playlist?list=PLmU0FIlJY-MkFrKtM0S0NLu-TxZa5jBIx

#calculus #limits #lhopital

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(0:00) When not to use L’Hôpital’s Rule
(1:20) lim_{h to 0}sin(4h)/(5h) (a 0/0 indeterminate form)
(4:09) lim_{t to 0}(e^(2t)-1-2t)/(3t^2) (a 0/0 indeterminate form)
(7:21) lim_{x to ∞}(3x^2+4x-5)/(2x^2-6x+7) (an ∞/∞ indeterminate form)
(10:19) lim_{x to 0+} x*ln(x) (a 0*∞ indeterminate form)
(13:43) sqrt(x)=x^(1/2) dominates ln(x) as x goes to ∞
(17:25) e^(0.1x) dominates 100x^2 as x goes to ∞
(18:51) lim_{x to ∞}(1+x)^(1/x) (an ∞^0 indeterminate form, use logarithms)
(21:38) lim_{x to ∞}(1+a/x)^(b*x) (a 1^∞ indeterminate form, use logarithms)
(26:44) lim_{x to 0}(1/x – 1/(e^(x)-1)) (an ∞ – ∞ indeterminate form)
(29:18) Graphical problem related to L’Hôpital’s Rule

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