Example: He came here to investigate George’s death. Definition: carry out formal inquiry to find out the truth. Example: He invested his money in business. ![]() I hope that this image helps you to understand the meaning of epsilon and delta. Definition: devote one’s time, money or energy to get profit. The distances of epsilon and delta (on either side of x = 3 and f(x) = 26, respectively) form a rectangle around the point (3,26). Find 69 ways to say ILLUSTRATE, along with antonyms, related words, and example sentences at, the world's most trusted free thesaurus. The function graph is shown in green, and the limit value is shown in red. Here is a graph of f(x) zoomed in very close to x = 3. Illustrate a point definition: If you say that something illustrates a situation that you are drawing attention to, you. These two distances away from 3 are the same distance (when rounded to four places, as required by the exercise), and that distance is delta. Here are a few definitions of ‘illustrate’: Oxford Dictionary says that to Illustrate is to Explain or make (something) clear by using examples, charts, pictures, etc. What value of x makes f(x) = 26.1? How far above 3 is that value of x? What value of x makes f(x) = 25.9? How far below 3 is that value of x? Having f(x) fall within 0.1 units of 26 means that it must lie somewhere within y = 25.9 to 26.1 That distance is the delta you're asked to find (first when epsilon is 0.1 units, and again when epsilon is 0.2 units). In other words, as x approaches 3 from the left (or, after x passes 3), within what distance of 3 does x need to be, in order for the value of f(x) to lie within 0.1 units above or below 26? If you want to ensure that the value of f(x) is within epsilon units of L, then how close to the value a does x need to be? That distance is delta. ![]() You can think of the first exercise as asking something like the following.
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