The Dirac delta-function obeys: see image 1 a). Prove that: see image 1 b). see image 2 c). Now briefly describe how this result can be generalised to g(x) with n simple roots at {x1,x2,...,xn}

7.0 refer to image

a) The roots of a degree 4 polynomial f(x) are 0, –1, 1, 1. Suppose f(2) = -1. Find a formula for f(x). b) On what intervals is the above function positive? c) On what intervals is the above function negative?

b) Find the order of Z=0 for the 25 1) 1+2-e² following functions: 3) (e ²²-1-2²) Sin³z 2) 6 sin(z ³) + z⁹-6z³

(b) Generate the graph of each of the following functions using the transfor- mation rules of graphs. i. f(x) = - cos(2x) in the interval [-27, 27] Rectangular Snip 1 g(r) = , sin (x -) in the interval [0, 27] ii. %3D

(3) Compute an approximation of f(x) = tanx by computing the coefficients Co, C₁, C2, C3 (a = 0). Then graph y = tan x and the obtained cubic polynomial in the same coordinate system. As you zoom on the origin (0, 0) do these two graphs get closer?

If f is a quadratic function such that f(0) = 9 and f(x) Fx + 1)3 is a rational.functian, find the value of f '(0). f '(0): Enter an exact number. Need Freip? Read It