1. Find a function f(x) that satisfies the following properties. (1) f(x) is continuous for all...

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1. Find a function f(x) that satisfies the following properties. (1) f(x) is continuous for all real numbers (2) f(x) 0 for all x > 0. > 0. (3) )" f(x)dx = 1 (this is computed as a limit, why?). +04-x (4) lim f(x) is not defined (in particular, the limit is not infinity, and this function does not have a vertical asymptote). You must explain why your function satisfies the properties (1)-(4) above. Hint: Draw an infinite sequence of triangular mountains, the first one with base on the interval [1/2, 1], the next on [1/4, 1/2], etc. As you get closer to 0, the height of the mountain gets higher and higher. Make sure to specify the height of each mountain. 1. Find a function f(x) that satisfies the following properties. (1) f(x) is continuous for all real numbers (2) f(x) 0 for all x > 0. > 0. (3) )" f(x)dx = 1 (this is computed as a limit, why?). +04-x (4) lim f(x) is not defined (in particular, the limit is not infinity, and this function does not have a vertical asymptote). You must explain why your function satisfies the properties (1)-(4) above. Hint: Draw an infinite sequence of triangular mountains, the first one with base on the interval [1/2, 1], the next on [1/4, 1/2], etc. As you get closer to 0, the height of the mountain gets higher and higher. Make sure to specify the height of each mountain.