8 2. Find the value of Σ by applying Parseval's identity to a suitable function on n=] the interval [-T, π, π].

Q: 12. For each n € N, define A, = [0, 1+] and B₁ = [0,1]. - =1 (a) Prove that U1A,, is an interval,…

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Q: Find an interval of t-values such that c(t) = (7 cos (t), 7 sin (t)) traces the lower half of the…

A:

Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

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Q: Evaluate fa² tan³ (2³) da + C

A: To integrate the given  function.

Q: 3. Use two rectangles of equal width to estimate the area between the graph of f(x) = x + cos(x) and…

A: Solved below.

Q: 6. Determine the intervals on which the following function is increasing or decreasing f(x) = sin r…

A: Note here we need a interval to find out where function increasing and decreasing because it is a…

Q: Choose a prime number, n, between 10 and 99, and using n, prove why the function ƒ(e (2πix)/n )=…

A: G is the group of nth roots of unity under complex multiplication.Zn is the group of integers mod n…

Q: Let L be any positive number. Consider the functions sin(x) and cos(x)

A: In this question, we find L for which the  given function f(x) = sin(x) and g(x) = cos(x) are…

Q: 4 Determine whether the given functions are LI or LD on the given interval. Use Wronskian and Show…

A: We have to check the given function is linearly independent or dependent.

Q: In the set of functions C[0, 7] determine what of these two functions is convex (f"(x) > 0) and what…

A: In this question we have to find the which function is concave or convex.