a Find values for the constants a, b, and c that will make (x) cos x and g(x) a bx cx 2 satisfy the conditions (0) g(0), (0) g(0), and (0) g(0) b Find values for b and c that will make (x) sin (x a) and g(x) b sin x c cos x satisfy the conditions (0) g(0) and (0) g(0) c For the determined values of...

a To make x cos x and gx a bx cx2 satisfy the conditions 0 g0 0 g0 and 0 g0 we need to equate the function values and their derivatives at x 0 0 g0 co ...

a. Find values for the constants a, b, and c that will make (x) = cos x

Question:

a. Find values for the constants a, b, and c that will make ƒ(x) = cos x and g(x) = a + bx + cx² satisfy the conditions ƒ(0) = g(0), ƒ′(0) = g′(0), and ƒ″(0) = g″(0).

b. Find values for b and c that will make ƒ(x) = sin (x + a) and g(x) = b sin x + c cos x satisfy the conditions ƒ(0) = g(0) and ƒ′(0) = g′(0).

c. For the determined values of a, b, and c, what happens for the third and fourth derivatives of ƒ and g in each of parts (a) and (b)?

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