For x ∈ [−2, 6],h(x) = 2x, j(x) = x2, and k(x) = 2x. 1. Represent...

For x ∈ [−2, 6],h(x) = 2x, j(x) = x2, and k(x) = 2x.

1. Represent each function with a sample table

2. Graph all three functions on the same coordinate system

3. Find the average rate of change for each function at x = . -1, x = 2, and x = 4

Expert Solution

milcah answered 2 years ago

Let p0 = 1+x; p1 = 1+3x+x2; p2 = 2x+x2; p3 = 1+x+x2 2 R[x]. (a)...

Let p0 = 1+x; p1 = 1+3x+x2; p2 = 2x+x2; p3 = 1+x+x2 2 R[x]. (a) Show that fp0; p1; p2; p3g spans the vector space P2(R). (b) Reduce the set fp0; p1; p2; p3g to a basis of P2(R).

1)For the function f(x)=6x^2−2x, evaluate and simplify. f(x+h)−f(x)/h 2)Evaluate the limit: limx→−6 if x^2+5x−6/x+6 3)A bacteria...

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Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. Lf (x) = Lg(x) = Lh(x) = (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function ? f g h since it is closer to ? f g h for a larger domain than it is to - Select - f and g g and h f and h . The approximation looks worst for ? f g h since ? f g h moves away from L faster...

1. For the equation x2+y2−2x−4y−11=0, do the following. (a) Find the center (h,k) and radius r...

1. For the equation x2+y2−2x−4y−11=0, do the following. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any.

Please find f(x') and f(x") for all: 1) f(x) = 3(x2 -2x)3/4(7 - 5x2)6 2) f(x)...

Please find f(x') and f(x") for all: 1) f(x) = 3(x2 -2x)3/4(7 - 5x2)6 2) f(x) = (y - x)4(y2 - x)3 3) f(x) = x7/3 + 16x3 + x 4) = f(x) = (x2 - x) / (y2 - y)

6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f ″(x) -...

6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f ″(x) - Determine any symmetry - Find the x- and y-intercepts - Use lim f (x) x→−∞ and lim f (x) x→+∞ to determine the end behavior - Locate any vertical asymptotes - Locate any horizontal asymptotes - Find all intervals where f (x) is increasing and decreasing - Find the open intervals where f (x) is concave up or concave down

Find (f −1)'(a). f(x) = 6 + x2 + tan(πx/2), −1 < x < 1, a = 6

(2) Jurian has preferences u J (x J 1 ; x J 2 ) = (x...

(2) Jurian has preferences u J (x J 1 ; x J 2 ) = (x J 1 ) 4 (x J 2 ) 2 . (a) Find his uncompensated demand for the two goods as a function of prices and her wealth w. (b) Find his compensated demand as a function of prices and her utility u. (c) Now suppose that Jurian interacts with Katinka in an exchange economy, where Katinka’s preferences are u K(x K 1 ; x...

x2 y" + (x2+x) y’ +(2x-1) y = 0, Find the general solution of y1 with...

x2 y" + (x2+x) y’ +(2x-1) y = 0, Find the general solution of y1 with r1 and calculate the coefficient up to c4 and also find the general expression of the recursion formula, (recursion formula for y1) Find the general solution of y2 based on theorem 4.3.1. (Hint, set d2 = 0)

Let R(x) = ( 2x^2 − 8x + 6 ) / (x^2 + 6x + 8)...

Let R(x) = ( 2x^2 − 8x + 6 ) / (x^2 + 6x + 8) a) Find all x such that R(x) is undefined. Find all x such that R(x) = 0. Evaluate R(0). Graph R(x) indicating all vertical and horizontal asymptotes and x and y intercepts. b) Find the intervals on which ( x^2 + 2x + 12 ) / (x − 2) ≥ 2x + 5.

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