48 The function f is defined by f(x) = for 3 <x< 7. The function g...
Suppose that the function F & G are defined as follows Suppose that the functions f and g are defined as follows. f(x) = 5-2x? g(x) = 2 - 6x (a) Find ( 2 )(-1). (a) Find (b) Find all values that are NOT in the domain of If there is more than one value, separate them with commas. (b) Value(s) that are NOT in the domain of
9. [7 points) Consider the function f(x) defined by f(x) = xeAs + B if x <3 C(x - 3)2 if 3 < x < 5 130 if > 5. C Suppose f(x) satisfies all of the following: f(x) is continuous at x = 3. • lim f(x) = 2 + lim f(x). 3+5+ 3-5- lim f(x) = -4. Find the values of A, B, and C. . 24-O
f(40) f(-3/2) f(-1) f(0) f(-3) Evaluate the piecewise defined function at the indicated values. if xs-1 if -1 <S1 x2 + 2x
(1 point) Find the critical numbers of the function f(x) = 2x3 + 6x2 - 48.. Answer (separate by commas): <= (1 point) List the critical numbers of the following function separating the values by commas. f(x) = 6x2 + 4 List the critical numbers of the following function in increasing order. Enter N in any blank that you don't need f(x) = 2x3 + 2x2 + 20
-2x +1, if x s -1 For the function f(x)= 2,1. ifxs- 6. I. Evaluate: a) f(-2) b) f(-1) c) f(o) II. Graph the function f(x) 5 2 -3 -5 7. Expand the following logarithmic expression using the properties of the logarith Assume all variables are positive. In Ve , find sin θ and tan θ, where θ terminates in the third quadra If cos θ 8. -2x +1, if x s -1 For the function f(x)= 2,1. ifxs- 6....
7) [f function g is defined by g(x) = Ta'an, xa, thon g'(1) = ? (A) 1 (B) 2 (C) 3 (D)O (E) Does not exist The graph of function g is shown below. Which of the following statements about function g is true? A) Atx=b, function g is differentiable. BY Atxa, function g is continuous, but not differentiable. C) Atx=a, function g is both continuous and differentiable Function g is not differentiable at any point. E) Atx=c, function g...
9. Graph the function defined by f(x) = 2 x +1 -3. Parent function: f(x) = x 1. f(x) = 2x +1 -3 Shift the graph to the left 1 unit 2. f(x) = 2 x +1 -3 Apply a vertical stretch multiply the y-values by 2) 3. f(x) = 2x+1-3 Shift the graph downward 3 units. 10. Graph the function defined by = (x) = -V3- x. Parent function y = x
beta is 1 2. ( 20p.) Consider the cubic spline for a function f on (0, 2) defined by 223 + ax2 + rx + 1 if 0 < x < 1 S(X) = (.x - 1)3 + c(x - 1)2 + d(x - 1) + B if i < x < 2 S(x) = { where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
4 -2 2. The function f is defined on the closed interval [-4,9]. The graph of f consists of a semicircle, a quarter circle, and three linear segments, as shown in the figure above. Let g be the function defined by g(x) = 3x + f(t) dt. (a) Find g(8) and g'(8). (b) Find the value of x in the closed interval (-4,9] at which g attains its maximum value. Justify your answer. (c) Find lim f'(x), or state that...
5. Let be the function defined by f(x) = -1 3 1.5 if r <0 if 0<x<2 if 3 < r <5 Find the Lebesgue integral of f over (-10,10).