Projected learning outcomes: Attempt to interpret and understand theorems regarding conti- nuity and limits to infinity. Specifically, one useful purpose for theorems proving that functions are continuous is to justify "plugging in" the number is approaching in the expression one wishes to take the limit of Problems 1. Use and cite the continuity theorems presented in lecture to find and justify the limit lim esin(r) 2 х—0

Q: Q 1: Explain the differences between continuity and uniform continuity with the help of examples…

A: The standard definitions of continuity and uniform continuity are given as. (1) Continuity-A…

Q: Find a bijective function: (use y= mx+b and show the details so I can know how to solve) a. [-3, 5]…

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Q: 5. Determine f"(a) for Ax) when a-1.

A: As per our guideline we can solve only one question at a time.please post other questions…

Q: Find the inverse of the relation Express your answer in terms of the new 'y'. (x+7)²+(y-6)² = 19

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Q: (f) Evaluate f(-1) and f(1). Can you conclude that there is no zero on the interval (-1, 1)? Explain…

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Q: Write down the domain of the function using set-builder notation. Sketch the domain of the function…

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Q: Determine the continuity of the following functions

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Q: Find a function f: Q → Q that is both surjective and injective but not the identity function.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.