7.7 EXERCISES 1. Let 1-(x) dx, where f is the function whose graph is shown. (a) Use the graph to...
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Let 1 = f(x) dx, where f is the function whose graph is shown. 3 (a) Use the graph to find L2, R2 and M2. L2 = (a) Use the graph to find L2, R2 and M2. L2= R2 = M2 = (b) Are these underestimates or overestimates of I? L2 is an underestimate. L2 is an overestimate. R2 is an underestimate. R2 is an overestimate. OM, is an underestimate. M2 is an...
5pt 1. Let g() = | f(t) dt, where f is the function whose graph is shown below on the interval [0, 5). The graph consists of two straight line segments. - - - ------ -1- - - - - - --1- - -1- - - - - - - (a) Find g(1) and g(3). (b) On what interval(s) is g(x) decreasing? (c) At what x-value(s) in (0,5) does the local maximum of g occur? (d) At what x-value(s) in...
Problem 12: Let g(x) = Sof) dt, where f is the function whose graph is shown in the figure. Estimate g(0.8(2), 8(4), 8(6), and g(8). s 2 Sketch a rough graph of g.
(4) Consider the function f(x) = V2 cos x. (1) Find the linear approximation L to the function f at a = (ii) Graph f and L on the same set of axes. (iii) Based on the graphs of part (ii), state whether linear approximations to f near a are underestimates or overestimates. (iv) Compute f"(a) to confirm your conclusion.
[(CO)] Let g(x) = f f(t) dt, where f is the function whose graph is shown. y Also 0,4 0,2 v -0,2 (a) At what values of x do the local maximum and minimum values of g occur? Xmin (smaller x-value) Xmin = (larger x-value) Xmax = (smaller x-value) Xmax (larger x-value) (b) Where does g attain its absolute maximum value?
Let f(x) = 2x + 8/x +1
(a) Find the interval(s) where the function is increasing and
the interval(s) where it is decreasing. If the answer cannot be
expressed as an interval, state DNE (short for does not exist).
(b) Find the relative maxima and relative minima, if any. If
none, state DNE.
(c) Determine where the graph of the function is concave upward
and where it is concave downward. If the answer cannot be expressed
as an interval, use...
Let gfx)-ft) dt where f is the function whose graph is shown. 20 30 (a) Evaluate gx) for x0, 5, 10, 15, 20, 25, and 30 g(0) = g(5) g(10)- g(15)- g(20)- g(25)- g(30)- (b) Estimate g(35). (Use the midpoint to get the most precise estimate.) (c) Where does g have a maximum and a minimum value? (d) Sketch a rough graph of g 25 25 35 35 35 35 x)
Let gfx)-ft) dt where f is the function whose...
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 <...
1. Let f be a function whose graph is shown below. 14 y 12 10 -14-12-10 - 2 2 10 12 14 TI -10 - 12 -14 (a) For which values r = a is the function f discontinuous. Use the formal defini- tion of continuity in your explanation (b) Does the function f graphed above have any removable discontinuities? Explain.
Please solve this problem completely.
(1) Length of graphs a) Let a path C be given by the graph of y - g(x), a b, with a piecewise C function g : [a,b] → R. Show that the path integral of a continuous function f : R2 → R over the path C is b) Let g: a bR be a piecewise Cl function. The length of the graph of g on (t, g(t)). Show that [a,b] is defined as...