Let f, g: R→ R be uniformly continuous functions on R. One of the following sentences is FALSE. Select one: a. If f(x) >0 for all x ER, then is uniformly continuous on R f b. fog is uniformly continuous on R C. f+g is uniformly continuous on R d. None of them е. If f and g are bounded on R, then fg is uniformly continuous on R

Q: Consider sets A and B with |A| = 7 and |B| = 4. How many functions f: A → B are surjective?

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Q: 3) Suppose that f is a continuous function and is defined on the interval [7,10]. If f(7) = 15 and…

A: if f(7)=15 f(10)=17 w real number  f(w)=15.8

Q: Exercise 3.3.7: Prove Corollary 3.3.12: Suppose f: [a,b] → R is a continuous function. Prove that…

A: We are to prove that the direct image f([a, b]) is a closed and bounded interval or a single number.

Q: 1. Show that the following functions f : R R are continuous. You should argue carefully from the…

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Q: 3. Let f : [2,5] → R such that f(x) et Is f uniformly continuous? Justify your answer. Answer:

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Q: A shopper buys cat food in bags of 3 lbs. Her cat eats 3434 lb each week. How many weeks does one…

A: Given that A shopper buys cat food in bags of 3 lbs. Her cat eats 3/4 lb each week

Q: Let f:R→R. If f is defined b then it is Cantindous. foo=2x+1 if X>o if X5o

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Q: Suppose that f and g are continuous functions on [a, b]. Show that if f = g a.e. on [a, b], then, in…

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Q: 44. Suppose that ƒ : [a, b] → [a, b] is continuous. Prove that there is at least one fixed point in…

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Q: Let f: R R be a function. Select ALL of the following statements which are equivalent to the…

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Q: Theorem. Suppose ƒ : [a, b] → R is continuous. Then it is uniformly continuous. 8. Prove this…

A: Let I=a,b If possible let  f be not uniformly continuous on I. Then there exist a positive ε0 for…

Q: Find the amount of money owed at the end of 5 years if $60,000 is borrowed at 7% per year compounded…

A: Here we have to find amount of money at the end of 5 years if money borrowed is $60, 000 at 7% rate…

Q: Find the matrices of the following linear transformations from R³ to R³. The orthogonal projection…

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Q: 4. Suppose f is defined on R and f satisfies |f(x) − f (y)| ≤ C\x − y|ª for all x, y € R. Here C and…

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Q: If f, g: R → R s.t. f and g are uniformly continuous. and bounded, then show that f.g is also…

A: Let f ,g are uniformly continuous And f and g are bounded

Q: Let m, n E Z. Prove that if m and n are odd, then m + mn +n is odd. Use the definition of even/odd…

A: If a number n is odd then  n=2k+1 for some k in integer.

Q: A fundamental fact is that if we are working on a closed, bounded inter [a, b], then any continuous…

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Q: Prove that f: R→ R is continuous. 2. Suppose that the function f : [0, 1] → R is continuous and that…

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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.