Exercise 2. Determine whether the sequence of functions (fn)n converges uniformly on S. 1 S = [0, 1]. S = [0, 1]. fn (x) = 1+ (nx – 1)²' fn(x) = na" (1 – x),

3 (4-x), 25x52 The error involved in making a certain measurement is a continuous rv x with pdf f(x) = b). Compute P(x > 0) c). Compute - 0 otherwise x > 0.5P(-1.2 (round to 4 decimal places) d). Compute P(x 0.5) (round to 4 decimal places)

Find the c in the MVT for f(x) = 5x-x2 , 1< x < 5. You might recall the MVT says that there is a c between 1 and 5 such that there is a c between 1 and 5 such that f'(c)=f(5)-f(1)                                                                          5-1

3. Let f: [-2, 2] → R be defined by I f(x):= ²+1' *€ [−2,2]. Find the intervals in which f is either increasing or decreasing. Find the maxima and minima of f.