Sketch the graph of a function f having the given characteristics. f(3) = f(9) = 0...
Sketch a graph of a function f having the given characteristics. f(0) = f(8) = 0 f'(x) < o if x < 4 f'(4) = 0 f'(x) > 0 if x > 4 f"(x) > 0
Sketch the graph that possesses the characteristics listed below. f'(3) = 0,1" (3) <0, f(3) = 5; f'(-1)= 0, f'(-1)>0, f(-1)= -1;f" (1) = 0, f(1) = 2 Choose the correct graph below. OA. OB O C. OD. 10
Find the area under the graph of g over [-2, 3] g(x) = -x? +5 when x 50 g(x) = x + 5 when x > 0
2. Draw a possible graph of the function described: (6 pts.) 10 O 00 07 f(-3)=4, f (2)=0 f'(-4)= f'(2) = f'(9)=0) f'>0 when x < -4 and x > 2 f' <0 when - 4<x<2 f">0 when -1<x< 5 or 9<x<10 f" <0 when x < -1 or 5<x< 9 or x >10 4 N NH -10 -8 -6 -4 -2 -2 4 07 8 10 -4 -6 -8 -10
Sketch a graph of the piecewise defined function. sz if x <3 f(x) = x 1 if x 2 3
Consider a periodic function f(x) given as -7, f(x) = { - < x < 0, 0 < x <, TT – I, f(x) = f(x + 27). i) Sketch the graph of f(x) in the interval –37 < x < 37. Then, deter- mine whether f(x) is even, odd or neither. (3 marks) ii) Hence, find the Fourier series of f(x). (12 marks)
7) (9 points) Sketch the graph of a function f(x) having the following given characteristics. Domain of f(x)= (-0,-5) U (-5,0) lim f(x)=–00, and lim f(x)=0 lim f(x) = 3 5 x-00 /'(x) >0 on (-00,-5) U (-5,0) / '(x) < 0on (0,0) /"(x) > 0 on (- 0,-5) /"(x) <0 on (-5,0) f(x) > 3 on (-0, -5) f(x) > 0 on (-3,3) f(x) <0 on (-5, -3) U (3,0) 8
9. The distribution function of a random variable X is given by 0, for r<-1, F(x) = { 271 -1<x<1, 1, 2 > 1. Find (a) P(Z < X < }); (b) P(1<x< 2).
For the given graph of f(x) below, use interval notation to express the solution to f(x) > 0. -7-675-- -2 -1 A) (0,0) B) (-5,2) u (5, 9) c) (0,3) D) (-00,-5) u (2,5)
Consider the random variable X whose probability density function is given by k/x3 if x>r fx(x) = otherwise Suppose that r=5.2. Find the value of k that makes fx(x) a valid probability density function.