Let f(x) = 1 = x3 3 The function above is: Increasing on the interval(s) Decreasing on the interval(s) + 14 x² + 32 N/W X

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Q: Let A= Which of the following the mullspace of A (b) (d) 2 ཀུག་ ༡) ། None of the above vectors is in…

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Q: Let y(x) be the solution of the initial value problem У y' = 1 + 1/4 + 5e-4/x X Then y(2) = 2 ln(k)…

A: Detailed explanation: Certainly! Let's go through the solution step by step in more detail, assuming…

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Q: h(x)= -36x^5-270x^4-480x^3-20   Can you show me how to find the intervals where h is increasing and…

A: Step 1: Find the first derivative of h(x) using the power rule:h(x)= -36x5-270x4-480x3-20h'(x)=…

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Q: I 5. Find the interval of convergence of the following. Be sure to test the endpoints of the…

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Q: Suppose that f(x, y) = √√25 — x² - y² at which {(x, y) | x² + y² ≤ 25}. - +r=5 Then the double…

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Q: Which of the following statements are true?(i) Every continuous function f : [a, b] → R has a…

A: This statement is true. It is a direct application of the Extreme Value Theorem, which states that…

Q: 3. Consider the following system of equations, x(t) = (x, y), - x' = (3-1)x 5y y' = 2x+(3+ 1)y (a)…

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Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

A: Step 1: Determine the quadrant bearing First, check to see if the vector is nearer to the South or…

Q: 4. (i) Let f R2 → R be defined by f(x1, x2) = 2x 8x1x2+4x+1. Find all local minima of ƒ on R². [20…

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Q: (b) Prove that for every positive integer n that 1 × 22+2 × 3² + 3 × 4² + ... ·+n(n + 1)² = n(n +…

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A: 1. Givenf(x)=x4+1x4​We have the following relation1+x1​=n=0∑∞​(−1)nxnSubstituting x4 in the place of…

Q: The differential equation bx [a y sin (5x) + 2e'* cos(4y) +mx²] dx + [cos(cx) + 2eb* sin(4y)] dy = 0…

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A: Step 1:Determine the Direction Vector of the Given LineStep 2:Find the Perpendicular Direction…

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A: Step 1: Step 2: Step 3: Step 4:

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Q: Sketch the graph of a function that satisfies all of the given conditions. f ′(x) > 0 for all x,…

A: Explanation:   f'(x) > 0 for all x: • This means the function is always increasing.  f''(x) >…

Q: 2. Consider the linear system x' = Aπ with = A-(G3). α where a -1. (a) Determine the eigenvalues in…

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Q: The differential equation x -4 -3 y² dx + (y² + x−³ y² + 6) dy = 0 is = ☐ non exact and has…

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Q: Question 1 The value of sin(5M) where M (0,0), (1, 1) and (3,0) is = O-0.091 0.126 -0.231 O -0.775…

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Q: 1. 3 points Estimate the area under the curve on the interval [-5,3] using the left-endpoint…

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