Determine which of the following pairs of functions are linearly independent. dependent 1. f(x) = x³ g(x) = |x|³ independent 2. f(0) = cos(30) dependent ♦ 3. f(t) = 3t² + 21t independent 4. f(x) = ³x " " 9 g(0) = 12 cos³ (0) — 9 cos(0) g(t) = 31²-21t g(x) = e³(x-3)

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Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 f'(2) = g'(2) =…

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Q: Find the first and second order derivatives of the function (a) f(x) = 0.001x5 -0.002x³ (b) G(r) =…

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Q: Find f. f(x) = f"(x) = cos(x), f(0) = 9, f'(0): = = 8, f "(0) = 6

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Q: The derivative F' (t) is graphed in the figure below. Given that F (0) = 12, calculate F(t) for t =…

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Q: Determine which of the following pairs of functions are linearly independent. 1. f(t) = 3t, g(t) =…

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Q: Determine which of the following pairs of functions are linearly independent. NO ANSWER + 1. f(x) =…

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Q: Find the second derivative of the following functions: a. f(x) = x5 + sin x b. f(x) = x² + == x c.…

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Q: Determine which of the following pairs of functions are linearly independent. 1. f(x) = x² g(x) =…

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Q: 2. What is the second derivative of f(x) = - ²x³²x²+6? f"(x) = 5x² - ²³√x f"(x) = 10x + √√√x+6 a. b.…

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Q: f (x) = x³ + 4xª + 3x³ – x² + & 1. ,2 -

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: Find f if f"(x) =2 + cos(x), f(0) = 10, f(t/2) = -5. f(x) = |

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Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

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Q: Let f(x) = X x - a Find the value of a so that f'(1) = 1 - 4

A: This question is based on Quotient rule of differentiation.