Let f be a 2T-periodic smooth function. Let dN(x) : 1 1 + [cos(x) + cos(2x) +...+ cos(Nx)] || OS for some positive integer N. Show that lim N→∞ f(x)ôN(x)dr = f(0)

Q: (1) Define the function f : RR by f(x) at a = 1. 2 X x2 x <1 x≥1° Show that f is continuous

A: অতএব, f a=1 এ অবিচ্ছিন্ন।Explanation:

Q: Use ϵ–δ arguments to prove:

A: Let's prove the continuity of each function using ϵ–δ arguments.(d) j(x)=3x−1 is continuous on…

Q: Let Assume that ƒ has a continuous derivative on [a, b]. Show that there exists a polynomial p(x)…

A: Given f has continuous derivative on a,b then for all ε&gt;0 there exist a polynomial qx such that…

Q: Determine the intervals of continuity for the function: f(x) = over the interval of 0 < x < 2n…

A:

Q: Find the value(s) of k such that the function f(x) is continuous on the interval (-∞, ∞). [x2 – 5x +…

A: f(x)={x2−5x+5,x&lt;k2x−7,x≥k

Q: Which of the following limits is equal to f1(x) (i.e. derivative of f), where f(x)=√x² +1 − 2x lim…

A:

Q: Find the following commutators by applying the operators to an arbitrary function f(x) 1. [2 cos(x),…

A: We have to find the commutators.

Q: Find f ∘ g ∘ h. f(x) = tan(x),  g(x) = x/x-2, h(x) = x1/3

A: We will find the composite function by working from the rightmost function

Q: The function f is a composite of two continuous functions: y = cos x and y = x 2, so f is continuous…

A: The function fx is a composition of functions y=cosx and y=x2and it is a continuous function.

Q: 3. Let fn(x) = ¹+cos(nx), x € R. Find f(x) so that fn → ƒ pointwise on R, then check whether fn → f…

A:

Q: Let D°[a, b] = set of all twice differentiable functions on the interval [a, b] with a continuous…

A:

Q: The domain of the function f(x) = arccos(x – 1) is equal to which of the following %3D intervals?…

A:

Q: Assume that f : R → R is defined via the assignment rule f(x) = e2x. We will use the notation that…

A: Given that the function f:R→R is defined by fx=e2x. The n-th derivative of a function f is denoted…

Q: Let G(x) be given, where f is continuous for all real t. Find (a) G(0), (b) G′(0), (c) G″(x), and…

A: (a) The given function Gx=∫0xs∫0sf(t)dtds where f is continuous for all real values of t. The…

Q: The limit represents the derivative of some function f at some number a. State such an f and a. lim…

A: Given that : The limit represent the derivative of some function f at some number a . limh→0 cos π+h…

Q: Let f. [-1/2,1/2] → R be given by f(x) = cos (x) * exp(x). There exists a unique inverse function g:…

A: We will use of chain rule

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.