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The graph of f(x) is shown. At which of the point(s) is f '(x) >0 and...
Exercise 6. Show that if f(x) > 0 for all x e [a, b] and f is integrable, then Sfdx > 0.
Using the graph of g(x) below, answer the following questions. F13 a) Where is g(x) > 0 ? (Enter an interval) b) Where is g(s) <0 ? (Enter an interval) c) Where is g(x) = 0 ? (Enter a list of values, separated by commas) d) Where is g'(x) > 0 ? (Enter an interval) e) Where is g'(x) < 0 ? (Enter an interval) fr/here is alr) - 02 (Enter a liet of valuee conarated hu commas) Summer20//gif/779d390a-6a66-3658-590a-d4a933422618_f102b983-2bb5-310b-bae4-8af4cdaf3863.png
For the given graph of f(x) below, use interval notation to express the solution to f(x) > 0. -7-675-- -2 -1 A) (0,0) B) (-5,2) u (5, 9) c) (0,3) D) (-00,-5) u (2,5)
Suppose f is continuous, f(0)=0, f(2)=2, f'(x)>0 and f (x) dx = 1. Find the value of the integral fro f-?(x) dx =?
1. Let F(x, y, z) = (-y + ,2-2,2-y), and let S be the surface of the paraboloid 2 = 9-32 - v2 for 2 > 0. oriented by an upward pointing normal vector. Note that the boundary of S is C, the circle of radius 3 in the xy-plane. Verify Stokes' Theorem by computing both sides of the equality: (a) (1 Credit) || (D x F). ds (b) (1 Credit) $F. dr
5. Let f(x) = arctan(In x) for all x >0. A graph of y = f(x) is shown in the figure. (a) Find the formula for the derivative f'(x). Then explain how you can deduce from this formula that f is invertible. (b) Find the formula for f-1(x), the inverse of f. (c) What is the domain and range of f-1? (d) Sketch a graph of the function y=f-1(x). (e) Now determine the value of (F-1)(0) using your results from...
If y = logga) f(x), where f(x) > 0 and g(x) > 0 are functions of x, find f'(x) On f(x) In g(x) g'(x) Inf(x) B. 8'(x) f'(x) f'(x)8'(x) f(x) OD_1'« n g(x) :'(x) Inf(x) g(x) In? g(x) O E. loga) f(x) ({*) – g'(x) In g(e)) flr
(1 point) Find the solution of x2y" + 5xy + (4 + 3x)y = 0, x > 0 of the form Yi = x" Ž Cpx”, n=0 where co = : 1. Enter r = Cn = n = 1,2,3,...
Could someone explain how these to get these phase portraits by hand with ẋ=y and ẏ=ax-x^2 especially for a=0 case where you have eigenvalues all equal to zero? 6.5.4 a>0 Sketch the phase portrait for the system x = ax-x, for a < 0, a = 0, and For a -(0 We were unable to transcribe this imageFor a>0 ES CS
Find the area under the graph of g over [-2, 3] g(x) = -x? +5 when x 50 g(x) = x + 5 when x > 0