please explain in detail 4 -11 23 4 Graph of f Let f be a continuous function defined on the closed interval -1Sxs4. The graph of f, consisting of three line segments, is shown above. Let g be...
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...
Graph of f Let f be the continuous function defined on (-1,8) whose graph, consisting of two line segments, is shown above. Let g and h be the functions defined by g(x) = h (2) = 5e-9 sin 2. -x +3 and (a) The function k is defined by k (x) = f(x) g(). Find k' (0) (b) The function m is defined by m (x) = 2007). Find m' (5). c) Find the value of x for -1 <...
(-5,2) (-2,-1) Graph of g The continuous function g has domain -5 < x < 2. The graph of g, consisting of two line segments and a semicircle, is shown in the figure above. The graph of g has a horizontal tangent at x = -1. Let h be the function defined by h(x) = S-29(t)dt for -5 < < 2. (a) Find the x-coordinate of each critical point of h on the interval -5 < x < 2. (b)...
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...
23. Let be a function defined and continuous on the closed interval (a,b). If f has a relative maximum at cand a<c<b, which of the following statements must be true? 1. f'(c) exists. II. If f'(c) exists, then f'(c)= 0. III. If f'(c) exists, then f"(c)<0. (A) II only (B) III only (C) I and II only (D) I and III only (E) II and III only
Graph off The function is defined on the interval -5 S figure above S where c and . The graph of which consists of three line segments and a quarter of a circle with center (3.0) and radius 2. is shown in the Forssxsc, leto be the function defined by g(x)= f(t)dt. Find the coordinate of each point of infection of the graph of Justify your answer
4. The function f is continuous on the closed interval (-2, 1). Some values of f are shown in the table below. --2 f(x) -3 -1 0 1 7 k3 The equation f(x) = 3 must have at least two solutions in the interval [-1,1) if k = a. 1 b. C. 2 CONN NICO d. 5. If k(r) is a continuous function over the interval (-2, 4) such that k(-2) = 3 and k(4) = 1, then k(2) 0...
- Let V be the vector space of continuous functions defined f : [0,1] → R and a : [0, 1] →R a positive continuous function. Let < f, g >a= Soa(x)f(x)g(x)dx. a) Prove that <, >a defines an inner product in V. b) For f,gE V let < f,g >= So f(x)g(x)dx. Prove that {xn} is a Cauchy sequence in the metric defined by <, >a if and only if it a Cauchy sequence in the metric defined by...
8. Consider the function f whose graph consists of four line segments and a semicircle as shown below. Define g(x) by g(x) = 5 f(t)dt. Note: The graph is of the function f. The graph of g is NOT shown to you. a) Find all values of x with –5 < x < 5 for which g'(x) = 0. Explain your reasoning. b) Find g(-1) and g"(-1). Show the work that leads to your answers. c) Find all values of...
1. Let f(x) be the 2T-periodic function which is defined by f(xcos(x/4) for -<< (a) Draw the graph of y = f(x) over the interval-3r < x < 3π. Is f continuous on R? (b) Find the trigonometric Fourier Series (with L = π) for f(x). Does the series converge absolutely or conditionally? Does it converge uniformly? Justify your answer. (c) Use your result to obtain explicit values for these three series: and , and 162 16k2-1" 16k2 1)2 に1...