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Lucky for us, this is kind of a fairly intuitive property of limits.
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 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.
The worksheets can be used as a test of mastery before moving on to subsequent video lessons in the series.
Limits Solved Problems
Every problem in the worksheets comes with a fully worked step-by-step written solution and answer key.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.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.What I want to do in this video is give you a bunch of properties of limits.And we're not going to prove it rigorously here.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.The “lim” shows limit, and fact that function f(n) approaches the limit L as n approaches c is described by the right arrow as: f(n) = L.We assume that To consider the limit of a sum of difference, select the limits individually and put them back with the corresponding sign.