2. For f(x) = f(x) = $2x+5, Xs1 14 + 3x, x>1 a. Find f (1) b. Find lim f(x) X1 C. Is f(x) continuous? Why, or why not?
cewise Functions e function, evaluate lim f(x). 2 1-2x²+x+3 f(x) = { 2x2 – 3x + 3 (-3x - 2 if if xs1 1<x< 6 if x26 below:
Suppose that the piecewise function J is defined by f(2)= {**** -1<<3 - 3x2 + 2x + 23, 2> 3 Determine which of the following statements are true. Select the correct answer below: O f() is not continuous at I = 3 because it is not defined at I = 3. Of() is not continuous at 2 = 3 because lim f(x) does not exist. f() is not continuous at I = 3 because lim f() f(3). ->3 f(x) is...
4. Find the following limits. 473 + 5x² - 2x+2) 273 - 2x + 100 203 - +3 (b) limz+03,3 - 2x2 – 3x + 2 (a) limz+ f (x +h)-f(x) 5. Find the derivative using the definition /' () = lim-0- (a) f(x) = 22 - 2 (b) f(x) = 2x + 3 6. Find the derivative using the formula including product rule and quotient rule (Don't use the definition in # 5) 3.- 2 (a) f(x) = 33...
2 Consider x2 if x <0 f (x) = 2x+ 1 if 0x < 2 (a) Determine whether f is continuous on the interval [0, 1]. (b) Determine whether f is right continuous on the interval [0, 1]. (c) Determine whether f is continuous on the interval [1,2].
The directional derivative of the function f(x, y) = 2x In(y) in the direction v =< 0,1 > at the point (1,1) is equal to 2. Select one: O True False
find the limit f(x) = 2x2 -3, if x-2 13-x, ifx < -2 then, determine if the function is continuous at x=-2
Suppose X is a continuous random variable having pdf (1+x, -1 < x < 0, f(x) = { 1 – x, 0 < x <1, lo, otherwise (a) Find E(X2). (b) Find Var(X2).
Evaluate the Riemann sum for f(x) = x2 + 2x – 1, 1<x< 4 with six subintervals, taking the sample points to be right endpoints.
Question 15 1 pt 1 Details -3.2 - 7 Given the function f(x) = - 2x2 + 2x + 11 32 +4 Calculate the following values: <-3 -3<<4 f(4) = f(10) = f(-3) = fl - 9) = f(1) = f(2) = Question 16 1 pt 1 Details Find the average rate of change for the given function over the indicated values of x. If necessary, round your final answer to two decimal places. y = 5x + 7, where...