Please state these definition and use detal and espilon: (fn) is a sequence if function: 1.What...

Please state these definition and use detal and espilon:

(fn) is a sequence if function:

1.What is the definition of (fn) is continuous?

2.What is the definition of (fn) is uniformly continuous?

3.What is the difference between the function continuous and the sequence of function continuous?

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

For the Fibonacci sequence, f0 = f1 = 1 and fn+1 = fn + fn−1 for...

For the Fibonacci sequence, f0 = f1 = 1 and fn+1 = fn + fn−1 for all n > 1. Prove using induction: fn+1fn−1 − f2n = (−1)n.

EXAMPLES OF THERMODYNAMIC STATE FUNCTION WITH DEFINITION

Conception of the Integral and convergence of the function 1. We know that if fn—->f is...

Conception of the Integral and convergence of the function 1. We know that if fn—->f is (point-wise or uniformly)and every fn in the interval is Riemann integral, then will f be Riemann integrable on [a,b]? please answer this question separately in pointwise and uniformly.

Let f1 = 1 and f2=1 and for all n>2 Let fn = fn-1+fn-2. Prove that...

Let f1 = 1 and f2=1 and for all n>2 Let fn = fn-1+fn-2. Prove that for all n, there is no prime p that divides noth fn and fn+1

1. Use the definition of convexity to prove that the function f(x) = x2 - 4x...

1. Use the definition of convexity to prove that the function f(x) = x2 - 4x + 8 is convex. Is this function strictly convex? 2. Use the definition of convexity to prove that the function f(x)= ax + b is both convex and concave for any a•b ≠ 0.

Fibonacci numbers are defined by F0 = 0, F1 = 1 and Fn+2 = Fn+1 +...

Fibonacci numbers are defined by F0 = 0, F1 = 1 and Fn+2 = Fn+1 + Fn for all n ∈ N ∪ {0}. (1) Make and prove an (if and only if) conjecture about which Fibonacci numbers are multiples of 3. (2) Make a conjecture about which Fibonacci numbers are multiples of 2020. (You do not need to prove your conjecture.) How many base cases would a proof by induction of your conjecture require?

a) State the definition that a function f(x) is continuous at x = a. b) Let...

a) State the definition that a function f(x) is continuous at x = a. b) Let f(x) = ax^2 + b if 0 < x ≤ 2 18/x+1 if x > 2 If f(1) = 3, determine the values of a and b for which f(x) is continuous for all x > 0.

Please use C++ 1. A Sequence of numbers and a sum is given as input. List...

Please use C++ 1. A Sequence of numbers and a sum is given as input. List all combinations of numbers that can add upto the given Sum. User input:- Enter numbers: - 1, 3,7,9,11 Enter a sum :- 20 Output: 11+9 = 20 1+3+7+9 = 20 2. Print absolute prime numbers between a given range:- Enter Range - 2,99 For eg Prime numbers are:- Prime numbers ==> 2,3,5,7,11,13,17,19,23 Absolute Prime numbers ==> 2,3,5,7,11,23 3. Write an encoder and decoder program,...

1. Use the function to find the following values (or state that they do not exist):...

1. Use the function to find the following values (or state that they do not exist): f(x) = 2 (x + 1)2 (x + 1)(x − 1)(x + 2) (a) State the domain of f(x). (b) Find any removable discontinuities (holes in the graph). (c) Find any Vertical Asymptotes. (d) Find any x-intercepts. (e) Find any y-intercepts. (f) Find the Horizontal Asymptote. Explain how you determined that this was an asymptote. (g) Graph f(x). Hint: It may help to find...

1. For the function f (x) = 2x² + 8 use the limit definition (four-step process)...

1. For the function f (x) = 2x² + 8 use the limit definition (four-step process) to find f′(x) . Students must show all steps (more or less four of them) to compute the derivative. Simply giving the derivative of the function will not receive much credit. 2. For the function f (x) = x² + 2x a. Find f′(x) . Students may use derivative rules to find this derivative. Show all work and clearly label the answer below. b....

Subjects