1. Apply Parseval's theorem to Q(t)= -{Q(+27) and use it to evaluate a sum rule for Σ1 k=1 |t|

Q: Form the interpolating polynomial of degree k that satisfies pG) (xo) = f(G) (xo) for 0<j< k.

A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

Q: Let f(x)=0 for x<1 and f(x)=(x−1)2 for x≥1. Find the smallest integer n such that f(n)(1) does not…

A: Ans:  for     n≥2 f(n)(1) does not exists.

Q: Find and classify the extreme values of f(r)=6r 4r over the interval (-2 21

A:

Q: (d) Prore that the function f(x) =X is Continous but not unifomly Continous on the intenal

A: Use the  absolun delta definition for uniformly continuous

Q: Let a(t), 2 < t< 8 be a positive function. Also, let the function 8(t) be defined as a'(t)/a(t) on…

A: We will find out the required expression.

Q: a)Find the average of the function f(x)= x² +1 on the interval [-1,2] Answer:

A:

Q: (b) Let I be an interval and f: IR be increasing. Show that fn(x) = f(x) +, defined on I, is…

A:

Q: Let f (x), −L < x < L, be an odd function that satisfies the symmetry condition f (L −x) = −f (x)…

A: Given: Let us consider the given function fx, -L&lt;x&lt;L and the condition fL-x=-fx. To find: An=0…

Q: 3. (a) Find a unit in Z[√2] which is not equal to 1 or -1. Hint: Use 1 (b). (b) (*) Show that Z[√2]…

A: The objective of the question is two-fold. First, we need to find a unit in the ring Z[sqrt(2)] that…

Q: Let f(t) = 2t² for -4 < t <4 and extend periodically. Compute: f(1) = f(5) = f(-4.5) = f(-8)= f(12)…

A: Periodic function: A function is said to be periodic with period T if f(x+T)=f(x).

Q: Find the absolute maximum and the absolute minimum of U(q) 20002 (15 5q)4 on the nterval 04.

A: First find the derivative of the given function and compute the critical points.

Q: (b) Let the function h : Z12 → Z12 be given by the rule h([x]) = [3] © [x]. (i) Compute h([5]). (ii)…

A:

Q: 1. Let f(x)= x on the interval [-7r, 7T. (a) Compute f42, given by 1/2 -T

A: To compute the L^2 norm of the given function, following the definition of the norm

Q: f(n)(x) = = (−1)n+13n (n − 1)! (3x + 5)

A: Consider a statement P(n), where n is a natural number. To validity of P(n) for every n, use the…

Q: A. Compute the bound B of the error when approximating f(x)=sin(x) with a polynomial of degree 1 in…

A: The given function is fx=sin x. Find the error bound for f approximating with a polynomial of degree…