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Infinite limits
- Class notes • 12 pages • 2020
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In general, a fractional function will have an infinite limit if the limit of the denominator is zero and the limit of the numerator is not zero. ... As x approaches 2 from the left, the numerator approaches 5, and the denominator approaches 0 through negative values; hence, the function decreases without bound and .
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Limits of functions
- Class notes • 8 pages • 2020
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A limit tells us the value that a function approaches as that function's inputs get closer and closer to some number. The idea of a limit is the basis of all calculus.
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Limits(rate of change & instanteous velocity)
- Class notes • 9 pages • 2020
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If f is a function of x, then the instantaneous rate of change at x=a is the limit of the average rate of change over a short interval, as we make that interval smaller and smaller. ... This is the slope of the line tangent to y=f(x) at the point (a,f(a))
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Finding limits by evaluation
- Class notes • 9 pages • 2020
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Evaluating Limits. Just Put The Value In. The first thing to try is just putting the value of the limit in, and see if it works (in other words substitution). Factors. We can try factoring. Conjugate. Infinite Limits and Rational Functions. L'Hôpital's Rule. Formal Method.
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Differentiation
- Class notes • 10 pages • 2020
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The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
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Home work problems with answers and notes
- Class notes • 89 pages • 2021
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Calculus 2 notes homework questions with answers and breakdown of each problem. Super organized and easy to learn everything in calculus 2.
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Limits by algebric manipulation and one sided limits
- Class notes • 14 pages • 2020
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A one-sided limit is the value the function approaches as the x-values approach the limit from *one side only*. For example, f(x)=|x|/x returns -1 for negative numbers, 1 for positive numbers, and isn't defined for 0. The one-sided *right* limit of f at x=0 is 1, and the one-sided *left* limit at x=0 is -1.
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The Fastest Way to Learn Everything You Need to Know About Limits
- Study guide • 3 pages • 2019
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This short document provides you with the all of the knowledge of mathematical limits you will ever need.
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The Fastest Way to Learn Everything You Need to Know About Limits
- Study guide • 3 pages • 2019
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This short document will provide you with everything you will ever need to know about limits.
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Continuity and Discontinuity
- Class notes • 8 pages • 2020
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A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function's value. ... Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal.
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