Use the functions f and g in C[-1, 1] to find (f, g), f, g, and d(f, g) for the inner product (f, g) = f(x)g(x)dx. f(x) = 3x, g(x) = ex (a) (f,g) (b) ||f|| (c) ||g|| (d) d(f, g)

Q: ) Is the function f(x) = differentiable on the open interval (-1,1)? x².

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Q: Determine a mapping of the form (x, y) (_) from y = f(x) for each of the following. y = 3f(2x)…

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Q: Determine Dx[x(x-2)²]

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Q: Find the domain of the square root function: w(x) = Vx + 25 x > 25 (-0, –25] [-25, о0) (-0, –5) U…

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Q: Show that the product rule works for the case f (x) = x2, g (x) = x3.

A: Given that, fx=x2gx=x3 We have to show that the product rule works for the case of given functions.

Q: D = {[x, f(x)]: (-1, 2), (0, 1), (1, 2), (2, 5), (3, 10)} Write the rule for f(x). x + 1 2x x² + 1

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Q: 2. Show that fxy and fyx are equal for the function f(x, y) = x²y sin(x + y). %3D xy. cos(xry) + 2xy…

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Q: 3. Find the Domain of the function : h(x)= x²-5 (a) (-00, -5] U,500) (b) R (c) (-0,5) (d) (-5,5]

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Q: dx (b): Evaluate the Jo (1+x)(2+x)/x(1-x)

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