5. 6 pt Determine whether the function f(x) is continuous and/or differentiable at x = 1....
check if e-1/4/ f(x) if x > 0 if x < 0 is differentiable at 0.
Determine if the following piecewise defined function is differentiable at x = 0. x20 f(x) = 4x-2, x2 + 4x-2, x<0 What is the right-hand derivative of the given function? f(0+h)-f(0) lim (Type an integer or a simplified fraction. I h h+0+
Is the function given by f(x) = continuous at x = 5? Why or why not? 5x+2, for x 55, 5* 5x - 18, for x>5, Choose the correct answer below. O A. The given function is continuous at x = 5 because the limit is 3. OB. The given function is continuous at x = 5 because lim f(x) does not exist. X-5 OC. The given function is not continuous at x = 5 because f(5) does not exist....
Assume that f is a continuous function on R such that f() = A | $(e) dt for some A > 0 and all x, and [f(x) < M for some M > 0 and all x E R. a) Prove that f has continuous derivatives of all orders on R, and for k > 1 that f(k) (x) = A(f(k-1)(x + 1) – f(k-1)(x - 1)).
11. Let X be a continuous random variable with density function fare-102 for 10 f(1) = lo otherwise where a > 0. What is the probability of X greater than or equal to the mode of X?
Determine if the limit exists, Graphically b.) lim X1 x2 + 3 2 x<> 1 x=1
8. Consider ar? +5 I <3 f(0) = 12.c +b > 3 Determine a and b such that f is continuous and differentiable at x = 3. )={
[ 10 pts.] 9. Use the alternative limit definition of derivative to determine whether the function 8sinh(x/2) ifx<2 f(x)= is differentiable or not differentiable at 2x²+x-1 if x2 x=c=2 Show all work !!!
Let f(x)= kx + 5 x-1 for x<2 for x > 2 . Find the value of k for which f(x) is continuous at x=2.
Please show work on how to solve? (49. Show that the function (x2 +3 for x < 1 f(x) = 10 - x for 1 < x <2 6x - x2 for x > 2 is continuous for x + 1, 2. Then compute the right- and left-hand lim- its at x = 1, 2, and determine whether f is left-continuous, right- continuous, or continuous at these points (Figure 17). y = 10 - x > 9+ y=6x - x2...