
Explore the informal and formal definition of limits, learn notation for x approaching c, one-sided limits, limit existence, and examples showing when limits exist, do not exist, or approach infinity.
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Learn to evaluate limits analytically by plugging in numbers when possible, then master factoring, conjugates for rationalizing, and the squeeze theorem with key limits like sin x over x.
Explore continuity and one-sided limits, define continuity at a point including holes or breaks, distinguish removable and non-removable discontinuities, and illustrate limits with intuition and examples.
Explore limits, infinity behavior, and vertical asymptotes in calculus, including one-sided limits, removable holes, and test-ready examples that show how x approaches c affects f(x).
Explore finding the slope of a function via secant lines and the limit as h approaches zero, leading to the derivative—the slope of the tangent line—with various notations.
Master explicit and implicit differentiation, compute dy/dx with the chain and product rules, and derive tangent lines for implicitly defined relations.
Master related rates in calculus 1 by differentiating sphere and cube formulas, using parametric equations, chain rule, and solving shadow and ladder problems via Pythagoras and similar triangles.
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Explore Rolle's theorem with continuous differentiable functions, equal endpoints, and a point c where f'(c)=0. See how the mean value theorem links average and instantaneous rates.
This is a complete course on Calculus 1 that is presented via lectures. For each of the regular lectures you will have an assignment as well as solutions to that assignment. At the very end of the course there is a final exam that you can take. In order to prepare for the final exam I have included a final exam review lecture that you can watch.
This course includes the following.
25 High Quality Lectures
25 Assignments with Solutions - one for each regular lecture.
A Final Exam Review Lecture
A Final Exam with Solutions
2 Additional Extra Lectures
The best way to watch these lectures is to be an active participant, the same way you would if you were taking a real class in an actual classroom. Here are some tips to make your learning experience better.
Work at your own pace and have fun with the lectures:) This is rule #1!
Take notes! You don't have to do this but it will greatly increase how much you actually retain from the lectures.
Work through the assignments at the end of each lecture. These were carefully constructed so that you have some way to test your knowledge.
Watch the Final Exam Review! This is a very good review and if you can understand this review then you can do very well on the final exam. The final exam was very carefully constructed so that this would happen.
I hope you enjoy these lectures. I think you will learn a lot from them, even if you don't take notes:)
Good luck and have fun!