Suppose f is a continuous function with f(-2) =4 and f(5) = -1. Use a substitution...
Problem 4. (6 pts) (a) Suppose that f(x) is a continuous function on 2,7], positive on (2,5) and negative on (5, 7). « [ r(a) dr = 11 and ſsaw) dr = 3, then ind ſis(2) dr. .10 f(x) (b) Suppose that is an even and integrable function. If "L" 3, . f(x) da = 5, then find L" (a) dr.
6.59. Let f be a continuous function on [a, b]. Suppose that there exists a positive constant K such that If(x) <K for all x in [a, b]. Prove that f(x) = 0 for all x in [a, b]. *ſ isoidi,
Suppose R is the shaded region in the figure, and f(x,y) is a continuous function on R. Find the limits of integration for the following iterated integrals. BD (a) [f $12,9)da = S, "Lº f12, y) dy de PH dA= JE JG f(x,y) dc dy I
Suppose f(x) is a given continuous function in -1,4] such that f(-1) and f(4) have different signs and consider the bisection method on f(x) using starting interval1,4]. (a) Bound the absolute error for the approximation c3o (Remember, we define co ao +bo)/2) (b) Use bisection method's bound on absolute error to determine which cn are guar- anteed to have absolute errors less than 10-9. Suppose f(x) is a given continuous function in -1,4] such that f(-1) and f(4) have different...
Suppose that f(1) = 1, f(4) = 5, f '(1) = 4, f '(4) = 5, and f '' is continuous. Find the value of 4 xf ''(x) dx 1 .
(1 point) Let f(a) be a function that is defined and has a continuous derivative on the interval (2,00). Assume also that f(3) = 6 \f (2) < 208 + 2 and f(xv)e 3/6 da = 5 Determine the value of $'(x)e-7/5 da
4. The function f is continuous on the closed interval (-2, 1). Some values of f are shown in the table below. --2 f(x) -3 -1 0 1 7 k3 The equation f(x) = 3 must have at least two solutions in the interval [-1,1) if k = a. 1 b. C. 2 CONN NICO d. 5. If k(r) is a continuous function over the interval (-2, 4) such that k(-2) = 3 and k(4) = 1, then k(2) 0...
(1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.
Suppose f is a continuous and differentiable function on [0,1] and f(0)= f(1). Let a E (0, 1). Suppose Vr,y(0,1) IF f'(x) 0 and f'(y) ±0 THEN f'(x) af'(y) Show that there is exactly f(ax) and f'(x) 0 such that f(x) one Hint: Suppose f(x) is a continuous function on [0, 1] and f(0) x € (0, 1) such that f(x) = f(ax) f(1). Let a e (0,1), there exists an Suppose f is a continuous and differentiable function on...
Question 4* (Similar to 18.1) Suppose f is a continuous function on a closed interval [a, b]. In class, we proved that f attains its maximum on that interval, i.e. there exists Imar E la, so that f(Imar) > f(x) for all r E (a,b]. We didn't prove that f attains its minimum on the interval, but I claimed that the proof is similar. In fact, you can use the fact that f attains its maximum on any closed interval...