Give an example of a function f: Σ* x N -> Z , where Σ =...
Give an example of a function f: Σ* x N -> Z , where Σ = {a,b} and where N represents the non-negative integers and Z represents the integers.
Homework Answers
There are multiple such function. Consider the input of the form
string 
and non negative integer N, and f outputs 
i.e. the difference of size of input string w with non negative
integer N. Clearly the output will be integer.
Ex:- f(abba,2) = 4-2 =2 and f(ababab,10)=6-10= -4
Please comment for any clarification
Consider the function f(x) = Σ (a) Where is f defined? (b) Where is f continuous? (c) Where is f ...
Consider the function f(x) = Σ (a) Where is f defined? (b) Where is f continuous? (c) Where is f differentiable? Consider the function f(x) = Σ (a) Where is f defined? (b) Where is f continuous? (c) Where is f differentiable?
Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1 < p. Show that the conjugate is where 1/p+1/g-1 Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1
Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1 < p. Show that the conjugate is where 1/p+1/g-1
Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1
(3) Let the function f(x) 0 if x Z, but for n e z we have f(n) . Prove that for any interval [a3]...
Advanced Calculus
(3) Let the function f(x) 0 if x Z, but for n e z we have f(n) . Prove that for any interval [a3] the function f is integrable and Ja far-б. Hint: let k be the number of integers in the interval. You can either induct on k or prove integrability directly from the definition or the box-sum criterion.
(3) Let the function f(x) 0 if x Z, but for n e z we have f(n) ....
(1) Let f be a multiplicative function satisfying Σ f(d)-n/0(n), where the sum is taken over all ...
(1) Let f be a multiplicative function satisfying Σ f(d)-n/0(n), where the sum is taken over all positive divisors of n, and ф is Euler's totient function. Use the Mobius inversion formula to prove that f(n) ."(n)/0(n)
(1) Let f be a multiplicative function satisfying Σ f(d)-n/0(n), where the sum is taken over all positive divisors of n, and ф is Euler's totient function. Use the Mobius inversion formula to prove that f(n) ."(n)/0(n)
(a) Use Exercise 26.2 to find an explicit formula for the function f(x)-ΣηΉ n- (b) Find the exact...
(a) Use Exercise 26.2 to find an explicit formula for the function f(x)-ΣηΉ n- (b) Find the exact value of Σ n-l 26.2 (a) Observe Σ001 nz"--for lx〈 1; see Example l. (1-z)2 (b) Evaluate . Compare with Exercise 14.13(d). 흙 ad Σ ( c) Evaluate 500. i (-1)"n _ n=1 n=1 3n
(a) Use Exercise 26.2 to find an explicit formula for the function f(x)-ΣηΉ n- (b) Find the exact value of Σ n-l
26.2 (a) Observe Σ001 nz"--for...
3a. Give an example of a function f(x) such that • f(x) < 0 • f'(x)...
3a. Give an example of a function f(x) such that • f(x) < 0 • f'(x) > 0 • f''(x) < 0 3b. Give an example of a function h(t) such that • h'(t) > 0 when t < −1 and t > 1 • h'(t) < 0 when −1 < t < 1 • h'(−1) = 0 • h'(1) is undefined
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B...
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2 marks] tured closed disk B.(0 )"-{ (z, y) E R2 10c x2 + y2 < 1}
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2...
where Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) < 00, then {x E X (z) > 0} is a countable set. (HINT: Show that for every k E N the set {x E X | f(x) > k-1} is finite.)...
where
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) < 00, then {x E X (z) > 0} is a countable set. (HINT: Show that for every k E N the set {x E X | f(x) > k-1} is finite.) f(x)-sup f(x) | F is any finite subset of X TEF
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) 0} is a countable set. (HINT: Show that...
Write a function that accepts as input a scalar x and an integer n and computes f(x), where f(x) = 1 + x + ... + x^n. For example, if x = 2 and n = 3, the function should return 1 + 2 + 4 + 8 = 15. Hi...
Write a function that accepts as input a scalar x and an integer
n and computes f(x), where
f(x) = 1 + x + ... + x^n.
For example, if x = 2 and n = 3, the function should return 1 +
2 + 4 + 8 = 15.
Hint: Use point-wise operations and the MATLAB sum function.
Your Function 1 1 function yf(x) 3 end Code to call your function
Your Function 1 1 function yf(x) 3 end...
4. (a) Indicate where the series is (i) absolutely convergent, n-1 where it is (ii) conditionally convergent, and where it is (iii) divergent. Justify your answers Find f,(z) if f(x) = arctan (e* ) +...
4. (a) Indicate where the series is (i) absolutely convergent, n-1 where it is (ii) conditionally convergent, and where it is (iii) divergent. Justify your answers Find f,(z) if f(x) = arctan (e* ) + arcsin V2x + 4. (b) (a) Set up (but do not evaluate) a definite integral that represents the area 5. of the region R inside the circle r = 4 sin θ and outside the circle r = 2. Carefully sketch the region R. (i)...
Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1 < p. Show that the conjugate is where 1/p+1/g-1
Let f: R"R be the function TL Σ Ι.rlp. f(z) where 1
Advanced Calculus
(3) Let the function f(x) 0 if x Z, but for n e z we have f(n) . Prove that for any interval [a3] the function f is integrable and Ja far-б. Hint: let k be the number of integers in the interval. You can either induct on k or prove integrability directly from the definition or the box-sum criterion.
(3) Let the function f(x) 0 if x Z, but for n e z we have f(n) ....
(1) Let f be a multiplicative function satisfying Σ f(d)-n/0(n), where the sum is taken over all positive divisors of n, and ф is Euler's totient function. Use the Mobius inversion formula to prove that f(n) ."(n)/0(n)
(1) Let f be a multiplicative function satisfying Σ f(d)-n/0(n), where the sum is taken over all positive divisors of n, and ф is Euler's totient function. Use the Mobius inversion formula to prove that f(n) ."(n)/0(n)
(a) Use Exercise 26.2 to find an explicit formula for the function f(x)-ΣηΉ n- (b) Find the exact value of Σ n-l 26.2 (a) Observe Σ001 nz"--for lx〈 1; see Example l. (1-z)2 (b) Evaluate . Compare with Exercise 14.13(d). 흙 ad Σ ( c) Evaluate 500. i (-1)"n _ n=1 n=1 3n
(a) Use Exercise 26.2 to find an explicit formula for the function f(x)-ΣηΉ n- (b) Find the exact value of Σ n-l
26.2 (a) Observe Σ001 nz"--for...
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2 marks] tured closed disk B.(0 )"-{ (z, y) E R2 10c x2 + y2 < 1}
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2...
where
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) < 00, then {x E X (z) > 0} is a countable set. (HINT: Show that for every k E N the set {x E X | f(x) > k-1} is finite.) f(x)-sup f(x) | F is any finite subset of X TEF
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) 0} is a countable set. (HINT: Show that...
Write a function that accepts as input a scalar x and an integer
n and computes f(x), where
f(x) = 1 + x + ... + x^n.
For example, if x = 2 and n = 3, the function should return 1 +
2 + 4 + 8 = 15.
Hint: Use point-wise operations and the MATLAB sum function.
Your Function 1 1 function yf(x) 3 end Code to call your function
Your Function 1 1 function yf(x) 3 end...
4. (a) Indicate where the series is (i) absolutely convergent, n-1 where it is (ii) conditionally convergent, and where it is (iii) divergent. Justify your answers Find f,(z) if f(x) = arctan (e* ) + arcsin V2x + 4. (b) (a) Set up (but do not evaluate) a definite integral that represents the area 5. of the region R inside the circle r = 4 sin θ and outside the circle r = 2. Carefully sketch the region R. (i)...
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