Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 8x² +17x - 10 on the interval [1,5]. Then find all values of c in the interval such that f'(c) = 0. Enter the exact answers in increasing order. To enter √a, type sqrt(a). C = C=

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A: This question is related to differentiation, We will solve it using given using given information.

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A: To determine that the differential equation is exact or not.

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A: Solve the following

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A: This question can be solved using the concept of differential equation.

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Q: 5. ²+²=2xy 6. 2x + 2y + 2y' + 1 = 0 dy dy 7.

A: Solution is here

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A: Given query is to find the angle between the vectors

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Q: where t is time in seconds and the dimensions

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Q: Q3) Find the integration by using Partial fraction method Y x² + 2x + 1 (x² + 1)² dx

A: The given integral is: I=∫x2+2x+1x2+12dx   As we know that; The Power Rule: ∫xndx=xn+1n+1+C And…

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A: To solve the initial value problem.

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Q: Q4/ 1- Evaluate: ffy sinx dy dx

A: According to company rule we can answer only first question and rest can be reposted.

Q: Direction: Prove by mathematical induction that k3²(+1)² for all n E N. Use the definition of the…

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Q: If the area under the curve, f(x), between [1, 5] is 12, what is the average value of f(x)?

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Q: 3

A: Solve the following

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Q: Q2/ Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

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Q: Consider the following homogeneous differential equation. xdx + (y-2x) dy = 0 Use the substitution x…

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Q: d dx -[x² tan x] d sin x dx 11+ cos x] 1 1 + cos x

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Q: Q1. Find the inverse of the following matrix by using Gauss-Jordan eliminations 0 1 21 -1 23 12₂₁ +1…

A: Here is the solution

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A: Here we have to check the convergence of given sequence

Q: 5. lim, A.7 Oi O о O. +D T 7x²+x-100 2x²-5x B 712 NIT D.2

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A: See the answer below

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Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

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Q: Which of the following graphs represents the function g(x) = x²(x + 1)(x − 2)? 2 4 2 * 0 4 0 O 4 2 P…

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Q: x-2 3. lim x-2x²-4

A: Here we have to find the limit of the function.

Q: If w = cos(xyz), compute for O-x²yz cos(xyz) - x sin(xyz) -x²yz cos(xyz) + x sin(xyz) O x²yz…

A: This question can be solved using the concept of partial derivatives.

Q: what should I write as the final answer

A: Let's solve given diffrential equation.

Q: Q2/Examine the following surface for maximum, minimum, and saddle points z = x² + y² + xy + 4x - 4y…

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