Functional Analysis Answers

Identify two problems in each category of the following time complexities and derive the complexity of these identified problems. (4+6 marks) O(n log n), and O(n2 ).

How p-adic norm is different from the real norm?

What is the p-adic absolute value or p-adic norm?

What do you mean by p-adic number?

Consider the functions h(x)=2x^2+x-1 and g(x)=4x-5 . The value of h(-1)-g(-1) is

value of 2-3*5+9 is

Calculate Time Complexity of following

(i)

F𝑜𝑟 (𝑖 = 1;𝑖 ≤ 𝑛; 𝑖 ∗ = 2)

{ 

𝑥 = 𝑥 + 1 

}

(ii)

𝑓𝑜𝑟 (𝑖 = 1;𝑖 ≤ 𝑛; 𝑖 + +)

𝑓𝑜𝑟 (𝑗 = 1;𝑗 ≤ 𝑛;𝑗 = 𝑗 ∗ 2)

{ 

… . 

… . 

}

What is the domain of the rational function f(x) = 2x²-7/ 3x + 5?

A. the set of all positive real numbers

B. the set of all real numbers except x= - 5/3

C. the set of all real numbers

D. the set of all real numbers except x= 5/3

Which of the following rational functions does not have a vertical asymptote?

A. g(x) = 2x+7/x+5

B. h(x) = 2x²+7/3x²-5

C. k(x) = 2x² - 7/3x-5

D. f(x) = 2/ x²+5

let H be finite separable hilbert space. show that H is unitarily isomorphic to cʳ for some r ∊ N.