Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the function f(x) = V1-x Oa 1N2 Ob12 Oc The unction does not satisfy the requirements of the mean-value theorem Odv2

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Q: Consider a continuous function f(x). The function has critical points at x = -7, x = -2, and x = 7.…

A: f(x) has critical points at x=-7 , -2 , 7Since f''(-7), f''(-2) is positive ⇒There is local minimum…

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A: To evaluate: ∫x3e4x dx

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A: Use additive property of integral

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A: From given data

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A: We have to simplify logarithm

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Q: 6. Use Laplace transforms to solve the initial value problems: (b) x" – x' – 2x = 0; x(0) = 0, x'(0)…

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Q: Express the shaded area of the region shown below by double integrals of order of integration (1)…

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A: Evaluate integral

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Q: Consider the tollowing Maclaurin series: (-1)"x2n (2n)! COS X = for all x e R. n=0 1. Let f(x) =…

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Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of does the curve has a…

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Q: Note Answer One Question Q1 The following data is provided for the velocity of an object as a…

A: Let's find.

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A: Solve the following

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A: Here we have to find the 3rd derivative of           y = -1/sin(3x)

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A: The given function,       fx=12x+12

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A: We need to find polar equation.

Q: B. Evaluate the following 1 dx 2. 2 tan(x)dx 3.

A: We have to slove above question

Q: Find f. f"(x) = -2 + 24x – 12x², f(0) = 6, f'(0) = 16 %D %3D f(x) = –x4 + 4x° 3 x + 16x + 6 %3D

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Q: 4. sin x dx 2.

A: Solving question number 4

Q: determine if the series diverges or converges

A: This question can be solved using the concept of convergence and divergence.

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Q: Given the function: f(x,y) = 4x*y² – 10p +y , find f a. 16x'y-60xy O b. 48x°y O C. 16xy – 10y O d.…

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Q: Is this series convergent or divergent?

A: This question can be solved using the concept of root test.

Q: 4. .2 + 2x) cos(2x) dx

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Q: Find the smallest number n of terms needed to obtain an approximation of the series 27ke-0.254² k=1…

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Q: -ions of the line through (-1, –2, 5)

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Q: 1. Water is being poured at the rate of 2 n m³/min. into an inverted conical tank that is 12-meter…

A: Let's find.