Zero from the left, our function seems to be approaching four. ![]() Of x as x approaches zero? This is, let's see, as we approach zero from the left, as we approach x equals Thing as the limit of h of x as x approaches zero over the limit of g of x as x approaches zero. So once again, using our limit properties, this is going to be the same So we have the limit as xĪpproaches zero of h of x over g of x. All right, so these are both, looks like continuous functions. And so negative one times one is going to be equal to, is equal to negative one. The function at that point because this is a continuous function. And it makes sense that theįunction is defined there, is defined at x equals zero, and the limit as x approaches zero is equal to the same as the, is equal to the value of Zero from the right, the function itself is approaching one. As we approach x equals zeroįrom the left, we approach, the function approaches one. We can see that, as weĪpproach it from the left, we are approaching one. As x approaches zero, as x approaches zero, the function is defined at x equals zero. Now what about h of x? Well, h of x we have down here. The value of the function seems to be approaching negative one. As we approach from the left, we're approaching negative one. So the limit here, this limit here is negative one. Right, the function seems to be approaching the But we see when we approach from the left, we are approaching the, the function seems toīe approaching the value of negative one right over here. So on f of x, as x approaches zero, notice the function itself So let's first think aboutį of x right over here. The same thing as the limit as x approaches zero of f of x times, times the limit as x approaches zero of h of x. And we know, from our limit properties, that this is going to be All right, we have graphical depictions of the graphs y equals f That means for a continuous function, we can find the limit by direct substitution (evaluating the function) if the function is continuous at \(a\).Find the limit of f of x times h of x as x approaches zero. In the figure, you can remind yourself of how we calculate slope using two points on the line: \( m=\text f(x) = f(a) \). ![]() ![]() If the line represents the distance traveled over time, for example, then its slope represents the velocity. It measures the rate of change of the y-coordinate with respect to changes in the x-coordinate. The slope of a line measures how fast a line rises or falls as we move from left to right along the line. Introduction Precalculus Idea: Slope and Rate of Change ![]() However, the content is essentially the same, and I've tried to put the videos in the correct location based on where the material was moved. This means that some of the section numbers I mention will no longer correspond to the same material, and screen-shots may look different. Note: The videos for sections 2.1-2.5 were recorded based on an older edition of the book.
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