The graph of the function f in the figure below consists of line segments and a quarter of a circle. Let g be the function given by g(x) = / f(t)dt. Determine a -1 values of c, if any, where g has a horizontal tangent line on the open interval (-9,9). Graph of f -10 8 7 432 10
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- a function is defined on the closed interval[-4,8] consists of two linear pieces and a semi circle defined by f(x)=3x integral from 0 to x g(t) dt find f(7) and f'(7) and find the value of x in the closed interval[-4,] at which f attains its maximum value. Justify your answerFilling in a function value The domain of ƒ(x, y) = e-1/(x2 + y2) excludes (0, 0). How should ƒ be defined at (0, 0) to make it continuous there?StokesTheorem.Evaluate∫ F·dr,whereF=arctanx/yi+ln√x2+y2j+k and C is the boundary of the triangle with vertices (0, 0, 0), (1, 1, 1), and (0, 0, 2).
- Find the area in square units of the region under the graph of the function f on the interval[-10,5] using the fundamental theorem of calculus then verify the result using geometry f(x) = 5True or False Plus. A. Any function cannot be integrated from limits a to b where c is a discontinuity given that a<c<b. B. Any improper integral not converging to a single value as an answer is considered diverging. Choices A. Both A and B is true B. Both A and B is false C. A is true, B is false D. A is false, B is trueUsing the First Derivative Test proved in the videos, prove the following version of the First Derivative Test: If f′ is continuous on the interval [a,b] and if f has exactly one critical point c then f has a maximum at c if f′(a′)>0 and f′(b′)<0 for some a′ and b′ such that a<a′<c<b′<b.
- Consider the function: f(x, y) = 2x3 + xy2 + 5x2 + y2 + 5 Find all the critical point of f. Use the 2nd derivative test to classify the critical points of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f has local maximum value(s) at (x,y) = f has local minimum value(s) at (x,y) = f has saddle point(s) at (x,y) =f (x, y) = (2h - y)(y - x^2) - critical point (0,0), is a local maximum of 8h. Q: Evaluate the value of f at this maximum.Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. x = 1 − y2, x = y2 − 1 The x y-coordinate plane is given. There are 2 curves, a shaded region, and an approximating rectangle on the graph. The first curve enters the window in the third quadrant, goes up and right becoming less steep, crosses the x-axis at approximately x = −0.71 crossing the second curve, changes direction at the point (0, 0.5), goes down and right becoming more steep, crosses the x-axis at approximately x = 0.71 crossing the second curve, and exits the window in the fourth quadrant. The second curve enters the window in the second quadrant, goes down and right becoming less steep, crosses the x-axis at approximately x = −0.71 crossing the first curve, changes direction at the point (0, −0.5), goes up and right becoming more steep, crosses the x-axis at approximately x = 0.71 crossing the first curve, and exits the window…