The graph of the function fis shown in the accompanying figure. (a) is f continuous at...
Graph of A continuous function fis defined on the closed interval - 4sxs6. The graph of consists of a line segment and a curve that is tangent to the x-axis at x-3, as shown in the figure above. On th interval Dexc6, the function fis twice differentiable, with f(x)>0. Is there a value of a -4sach, for which the Mean Value Theorem applied to the interval (a 6), guarantees a value ca cx6, at which f'(c) = ? Justify your...
Let f be defined on an open interval I containing a point a (1) Prove that if f is differentiable on I and f"(a) exists, then lim h-+0 (a 2 h2 (2) Prove that if f is continuous at a and there exist constants α and β such that the limit L := lim h2 exists, then f(a)-α and f'(a)-β. Does f"(a) exist and equal to 2L? Let f be defined on an open interval I containing a point a...
ha (predict the tuto por certain town 5. A function fis said to be continuous at x = a if f(a) is defined, if lim f(x) exists, and if lim/(x) = f(a). Use this definition to explain why the following function is not continuous at x = 2. Include in your explanation an accurate sketch of this function. Also be sure to state specific values of "a", lim f(x), and f(a) in your response. Slx - 21 if x #...
Problem 2. (12 pts) The graph of a function fis given below. Answer the questions that follow. 110 6 2- 5 -6- - X-2 (i) (6 pts) Find the following limits. If a limit is infinite or does not exist, specify so. (Ipt each) a) lim f(x) = b) lim f(x)= c) limf(x) = d) lim f(x) = e) lim f(x) = g) limf(x) = (2 pts) Does f have any asymptote(s)? If yes, what kind? Write their equations. (iii)...
-/7.14 points WANEAC7 3.1.035. 0/6 Submissions Used The graph of fis given. Use the graph to compute the quantities asked for, if a - 6. HINT (See Examples 4-5.1 (If you need to use or -- enter INFINITY or -INFINITY, respectively. If an answer does not exist, enter DNE.) (a) lim f(x) (b) lim f(x) Need Help? Wh Talk is a Tutar | -/7.14 points WANEAC73.1.039. 0/6 Submissions Used The graph of f is given. Use the graph to compute...
6. (10 points) The graph of a function fis given below. O O . a. For which values of x in the interval (-4,4) is f not continuous? Give the type of discontinuity Gump, infinite or removable) in each case. b. For which values of x in the interval (-4,4) is f not differentiable? c. Give the value of the following: lim f(x) it. limf(x) ill. lim 1.
4. [-/1 Points] DETAILS LARCALC11 3.2.006. Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that fe 8(+) = N(2 – 2+)'. 1.1,1) None of these. f(a) does not equal f(b) for all possible values of a and b in the interval [-1, 1). Fla) does not equal f(b) for any values in the interval [-1, 1). There are points on the interval [a, b] where fis not continuous. There are...
6. (10 points) The graph of a function fis given below. 2 a. For which values of x in the interval (-4,4) is f not continuous? Give the type of discontinuity (jump, infinite or removable) in each case. b. For which values of x in the interval (-4,4) is f not differentiable? c. Give the value of the following: i. lim f(x) ii. limf(x) ill. lim f(x) 22+
6. (10 points) The graph of a function fis given below. O O a. For which values of x in the interval (-4,4) is fnot continuous? Give the type of discontinuity (jump, infinite or removable) in each case. b. For which values of x in the interval (-4,4) is f not differentiable? c. Give the value of the following: i. lim f(x) lll. lim f(x) X-2 X-2 X-2
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...