Limits Solved Problems

In Mathematics, a limit is defined as a value that a function approaches, as the input approaches to some value.Limits are important in calculus and mathematical analysis and used to define integrals, derivatives, and continuity.

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And what's neat about it is the property of limits kind of are the things that you would naturally want to do.

And if you graph some of these functions, it actually turns out to be quite intuitive.

Which is equal to, well this right over here is-- let me do that in that same color-- this right here is just equal to L. The limit as x approaches c of f of x minus g of x, is just going to be L minus M.

It's just the limit of f of x as x approaches c, minus the limit of g of x as x approaches c. And we also often call it the difference rule, or the difference property, of limits.

This fact works regardless of number of functions we seperated by “ ” or “-”.

Worksheet 1: Evaluating Simple Limits with Substitution - Part 1Worksheet 2: Evaluating Simple Limits with Substitution - Part 2Worksheet 3: Evaluating Limits by Factoring - Part 1Worksheet 4: Evaluating Limits by Factoring - Part 2Worksheet 5: Limits Involving Trig Functions Worksheet 6: Tangent Lines, Velocity, and Limits Worksheet 7: Formal Definition of a Limit Worksheet 8: Limit Laws Worksheet 9: Using the Limit Laws Worksheet 10: The Squeezing Theorem Worksheet 11: Left Hand and Right Hand Limits - Part 1Worksheet 12: Left Hand and Right Hand Limits - Part 2Worksheet 13: Continuity These worksheets are to be used along with the Calculus 1 Limits video lessons.The worksheets can be used as a test of mastery before moving on to subsequent video lessons in the series.Every problem in the worksheets comes with a fully worked step-by-step written solution and answer key.These revision exercises will help you practise the procedures involved in finding limits and examining the continuity of functions.All these topics are taught in MATH108, but are also needed for MATH109.The limit of a sequence is further generalized in the concept of the limit of a topological net and related to the limit and direct limit in theory category.A limit is normally expressed as It is read as “the limit of f of n, as n approaches c equals L”.Now given that, what would be the limit of f of x plus g of x as x approaches c? This is often called the sum rule, or the sum property, of limits.Well-- and you could look at this visually, if you look at the graphs of two arbitrary functions, you would essentially just add those two functions-- it'll be pretty clear that this is going to be equal to-- and once again, I'm not doing a rigorous proof, I'm just really giving you the properties here-- this is going to be the limit of f of x as x approaches c, plus the limit of g of x as x approaches c. And we could come up with a very similar one with differences.And finally-- this is sometimes called the quotient property-- finally we'll look at the exponent property.So if I have the limit of-- let me write it this way-- of f of x to some power.