Theorem 1 in Section 2.4 states the following: "If f and g are continuous functions, then f + g is continuous." Does it follow logically that if f and g are not continuous, then f + g is not continuous?

Q: If F is a continuous on the set of real numbers, then (A True (B False

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Q: If F is a continuous on the set of real numbers, then A True B) False

A: Note that we can take constant outside of an integration. So, the given statement is true.

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Q: Iff: X→ Y is a function and F is a nonempty family of subsets of y, then o(ƒ˜¹ (F¹)) =ƒ˜¹ (0 (F)).

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Q: | if x#3 6. %3D 15. Show that if the function g is defined by g(x) = if x=3 then g is not continuous…

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Q: QUESTION 11 Let f:X-Y be a continuous function. If X is disconnected then so is f(X). O True O False

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Q: 9. Suppose g is a function continuous at c and g(c) > 0. Prove that there exists o>0 such that g(x)…

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Q: b) If the functions f : R → R, g : R → R are Lipschitz continuous, then the function ƒ o g is also a…

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Q: 1- DETERMINE A AND BEC FOR THAT THE FUNCTION: (f:C+a=+b -2 +az +b f(=) = IF = #1-i, 2-1+i (f(1– i)…

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Q: Find a function f and a real number a such that

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A: Given:If f and g are even functionthen fg is also an even function

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Q: Theorem 1. If f : R → R is a C² function, then f is conver if and only if f"(x) > 0 for every x E R.

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Q: 3. (a) Prove that iff is continuous everywhere, then |f| is continuous everywhere.

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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.