check if e-1/4/ f(x) if x > 0 if x < 0 is differentiable at 0.
5) In C.), with inner product <f,g> [f(x)g(x)dx, let f(x) = x², g(x)= x', a) Compute< x², x? >; 0 b) Find the “angle” between the two functions.
F. dr Find a function of such that of 8 and then evaluate where F(x, y) = < 3 + 2kg", 2y) and C is any smooth curve from (-2, 1) to (1,2).
The graph of f(x) is shown. At which of the point(s) is f '(x) >0 and f "(x) < 0? List all points where both f '(x) > 0 and f '(x) <0. If there is only one point where this is true, list it. If there is more than one point, list them all and separate the answers by commas. If there is no such point, type N.
(1 point) If f(x) = 3x5 – 10x3 + 5, on what intervals is f" (x) > 0? Enter the (disjoint) interval(s) below using 'U' for union, 'inf' for wo, and '-inf' for – if necessary.
Problem 2. Let f be a self-map on a set X. For x,y e X define x ~ y if and only if f"(x) = f(y) for some integers n, m > 0. Show that ~ is an equivalence relation.
this curve, with X - axis rotation, calculate surfacea area y=e-72, (x > 0)
All work please Evaluate: SỐ 9(x) dx, where g(x) = x2 for x 5 2 = 5 + x for x > 2 Find the average value of y = 4x3 + 2x over the interval [–2, 1]
8. Let f (x) e, 0 > 0; x> 0 (1 1 +e (a) Show that f(x) is a probability density function (b) Find P(X> x) (c) Find the failure rate function of X
3) Given vector field F(x,y,z)=<y, xz,x? >. Find N dr where T is the path around the triangle with vertices (1,0,0),(0,1,0) and (0,0,1) traced counterclockwise (when viewed from above.)