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![Q1: Find the Fourier coefficients and Fourier series of the triangle
function f(x) defined by
+x if -n≤x≤0
f(x)=
and defined on the interval
+ x,
if
0<ST
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- Graph and find the Fourier coefficients of the following functions f (x): - T/2 < x < Tn/2 1/2 < x < 3n/2 1 a) f(x) = { -1 b) f(x) = { "** -π3. Consider the equation f(x) = x³ - 2x² – 11x + 12 on the interval [1.78, 8.25]. (a) Find the minimum number of iterations required to find the root of the given equation within the error bound of 1 x 10-3. (b) Show 5 iterations using the Bisection Method to find the root of the above function within the interval [1.78, 8.25].Find the the Taylor's polynomial P2(x)for the function f(x) = 4x²e¬2« about xo = 0 and hence find f(0.5). Find the upper bound for the error R2(0.5). Answer:Consider the following. -2 SxS -1, (x) -7x, -1Find the first four of the Taylor the function 1/x about the point a = -1 (Your answers should include the variable x when appropriate) 1/x = ?+?+?+? I got 1/x= -1/0!+ (x+1)/1!+-2(x+1)^2/2!+(6(x+1))/3! However, (x+1)/1! And (6(x+1))/3! Is incorrect. Please help me.Show that the equation x3 - 17x + c = 0 has at most one solution in the interval [-2, 2]. Let f(x) = x - 17x + c for x in [-2, 2]. If f has two real solutions a and b in [-2, 2], with a < b, then -Select--- polynomial f is continuous on [a, b] and differentiable on (a, b), -Select-- v. Since the ) implies that there is a number r in (a, b) such that f'(r) = 0. Now f'(r) = . Since r is in (a, b), which is contained in [-2, 2], we have Irl < 2, so r? < 4. It follows that 3r2 - 17 ?v 3 ·4 - 17 = -5 ?v 0. This contradicts f'(r) = 0, so the given equation cannot have two real solutions in [-2, 2]. Hence, it has at most one real solution in [-2, 2].Given graph of f(x)=2x^3-5x^2-7x+6. Find all the roots of f(x) by using bisection method with |b-al=1 * 20- -1.427 and 0.639 3.288, 0.639 and -1.427 3.321, 0.639 and -1.427 3.321 and -1.427Consider the function 2: {1,2, 3, 4} → {0, 1,2} defined as follows: N:n → (2n + 2) mod 3 ( ..1) Draw an arrow diagram to represent the function above (like in problem [J]). ( .2) N(2) (fill in the blank). ( '.2) What is the inverse image of 2?1. Express f(x) by the Fourier series where f(x)= {, 2, -7Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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