Find the general solution of the given differential equation. y" + 2y' + y = 14e-t
1. (a) Find the standard trigonometric Fourier Series S(x) of f()co(x/3), - -< I. (b) Graph S(x) for-3r < x 3π (c) Show that the series S(x) converges uniformly on R 1. (a) Find the standard trigonometric Fourier Series S(x) of f()co(x/3), - -
What should be the value c so that the function f random variable X? 1*(x2 +93), for x = 0, 1, 2, 3 can serve as a probability distribution of the discrete
Show that if f (x - 1) = -f 6 - x), S“ f (x - 2) dx = 0. Hint: You may find it useful to make the variable substitution, u = (x - ).
4. For this question, define f(x) = (x - 1)e-(0-1). (a) Find f'(x) and f"(x). (b) Find where S is increasing and where / is decreasing (e) Find where S is concave up and where / is concave down. (a) Find all critical points of . For each point you find, explain whether it is a (relative) maximum, a (relative) minimum or neither. (e) Find all points of inflection of f. For each point you find, explain why it is...
1. For f(x) = 924 – 2x a) Find the critical value(s). b) Find the open intervals over which the function is increasing or decreasing, c) Find the point(s) of any relative maxima or relative minima.
5. Find the transfer function X (3) F(s) and X:(5) F(s) for the mechanical system below Kj = 4 N/m *(1) K2 = 5 N/m 00002 0000 = 3 N-s/m M =1 kg|fv2 = 3 N-s/m M2 = 2 kg Svz = 2 N-s/m E
Find the interval(s) on which f (x) = 2x2 – 3x2 – 12x + 1 is concave up.
Let f(x) = 4 x² +7 x – 3 (a) Find the vertical asymptote(s) of the graph of f(x). x = (b) Find the horizontal asymptote(s) of the graph of f(x). y = (c) Find the slant asymptote(s) of the graph of f(x). y = Note: Use a comma-separated list for multiple answers or the word NONE if no such asymptote exists.
Question 5: (1 point) f(x) = + x - 18, find S (1) (a) 215 (b)-875 (c)-115 (d) 1/5 (e) -215