Question Using Rolle's theorem for the following function, find all values c in the given interval where f' (x) = 0. If there are multiple values, separate them %3D using a comma. f(x) = -3x² – 6x + 4 over [-3, 1] Provide your answer below:

Q: (-1)" V2n2 + 5 Given: power series (x+ 1)" n=1 Determine if the resulting series of constant terms…

A: To solve the following problem

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Q: 5. What is the derivative of 2x*? A. 8x3 В. 2 С. х D. 0 6. Consider the function f(x)=|x-21 at x-2…

A: Since you have posted multiple questions i can do first three question as per our company guidelines…

Q: (-3)"(x – 2)" Vn+2 Consider the power series 1. Use Limit Comparison Test to show that the series…

A: 1.when x=53∑n=0∞ (-3)n(-3)nn+2∑n=0∞ 1n+2can be compared to∑n=0∞ 1nc=limn→∞ anbn=limn→∞ n+2nlimn→∞…

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A: we have to find length range for the given rectangle.

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A: Comparison test: Let ∑n=1∞an  and ∑n=1∞bn be two series such that an≤bn ∀n∈N If ∑n=1∞an divergent…

Q: 7. F- dr from (0,0) to (3,9) along the curve y=x' if F(x, y, z) = 4 xyi + 3xy'j Evaluate

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Q: 1 In solving the antiderivative of f(x) 2-3sin(x) by miscellaneous substitution, the substitution…

A: Given problem:-

Q: determine if the series diverges or converges

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

Q: The concentration of a drug t hours after being injected is given by C(t)=0.8t / t^2+68. Find the…

A: This question can be solved using the concept of maxima and minima.

Q: A rectangular poster is to contain 338 square centimeters of print. The margins at the top and…

A: Here we have to use the concept of derivatives.

Q: O Fnd the pemainders when @ x³ - 2xx +5x +8 is divided by x-2, (b) x+ x -9 s OC +1 dwided by is…

A:

Q: 8. 6x° cos (x³) dx

A: ∫ x8cosx3dx

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Q: Let slx) = tan X %3D 3, ind ) tanx dx using Lebesgue in tegral.

A: To evaluate the integral.

Q: 4-x Q3) Evaluate triple integral , S S* dz dx dy.

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Q: Evaluate the integral 2x 4)

A: ∫1e2x-452dx=∫1ex2-452dxSubstitute…

Q: 6. Use Laplace transforms to solve the initial value problems: (a) x" + 9x = 0; x(0) = 3, x'(0) = 4…

A: Given x''+9x=0, x0=3, x'0=4

Q: 9– 4x2 Evaluate: 4.x2 + 2 sin () +C A 6/ f (x) = 9-4x2 - 2.x sin () + C B f (x) = - -1 ( 2r 9-4x2+2x…

A: here we do integration using parts ∫ fg' = fg -∫f'g f = 9-4x2 g' = 1/x2 f' = -4x/9-4x2 g = -1/x ∫…

Q: x² +64 Using trigonometric substitution, given dx, the simplified form of the integral is: x2 […

A: Use trigonometric substitution,

Q: given series is convergent 2"

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A: I am attaching image so that you understand each and every step.

Q: y= ( х-6 3 1. у %3 Зx+4,

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Determine whether the following series is convergent or divergent full solution pls and write what…

A: Let's find.

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Q: The task is to evaluate the function using reversed order of integration. •1 eee-x dx dy 1 Jlny

A: Change of order.

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Q: Direction: Find the antiderivatives of the following functions using substitution rule. 1. S(5x +…

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Q: 1Evaluate the ff. integrals using either integration by pants, trigonometric integrals , trig on o…

A: As per guidelines of bartleby, we are instructed to solve only first 3 subparts of a problem.

Q: х2 - бх + 9 V6x – x2 хр

A: Given problem:- ∫ (x2 -6x+9)/√(6x-x2) dx

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A: Answer is in step 2.

Q: 4. sin x dx

A: As you mentioned problem number 4 solved

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Q: 10. [ tan 0 de 12.f cos do 3

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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: The differential equation dy/dx = y(y+6) has initial condition of y(0) = 3 What is y(1)? Multiple…

A: Given

Q: For the sequence defined by: a1 = 3 1 - 3 An аn +1 Find: a2 аз = II II

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Q: ) Solve the D.E dy + (xy – xy²)dx = 0

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Q: Solve the differential equation y’=xsqrt(y); y(0)=1

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Q: What is the general solution of the system x − 2y + z = 3 2x − 3y + z = 8   Multiple choice…

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Q: 220° 12 сm 70° X =

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i+4 sin(t)j+ tk;…

A: Answer in the box are correct

Q: (NAS 2) Find the directional derivative of f(x, y, 2) = 2 + y + 4.xz at the point (1,-2, 2) in the…

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Q: V. Let f(x) be a differentiable function such that for all æ > 1, • f(x) > 1, • f'(x) < f(x) and lim…

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Q: 1. The derivative of the sum or difference of two differentiable functions is to the sum or…

A: The solution is given in the next step.

Q: Solve if the improper integral below diverges or converges. If it converges, solve for the value. 1…

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