Find the average value of the function f(x) = over the interval [0, 6] and find c such that f (c) equals the average value of the function over [0, 6].

Q: Use a system of linear equations with two variables and two equations to solve. A number is 8 more…

A: The solution is given below

Q: 12. Integral x² dx x³ +4

A: Given the integral,        ∫x2 dxx3+4

Q: d dx (f³x²) = ○ 6x63x² (In b) ○ 6³x² (6 ln b) 6x6³x² ○ xb³x² (ln(6b))

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Q: The fourth left-endpoint in a partition of [0, 3] with Ax = 0.5 is

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Q: Find f'(0) if f(x) = a; a, b, c, d constant bc-ad O d² ad-bc (c+d)² ad-bc d² ad+bc d²

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Q: Determine the number of points of intersection for the planes: T₁: 3x-6y + 12z - 6 = 0 and 7₂: 2x -…

A: We want to find number of points of intersection of two planes.

Q: Consider the following sequence x₁ = √₁, x₂ = √1 + √I, x3 = √1+√₁+√₁ Evaluate lim xn (No credit for…

A: The given sequence,x1=1, x2=1+1, x3=1+1+1

Q: Complete the table for the equation y=x-2, and graph the equation. X -2 - 1 0 1 2 Use the graphing…

A: line

Q: Q1A) The vectors A = 3i + j + 4k, B = 2i - 3j - k, find vector normal to A and In plane of A and, B.

A: Solution is given below:

Q: 4: Find the indefinite integral of f(u) = -1-3√ =

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Q: Determine if the series. HE 10 n² 4n+3 74 converges or diverges. If the series converges, give its…

A:

Q: Evaluate x/12 0 14√/1- cos 12x dx.

A: Given, ∫0π4141-cos12xdx

Q: a) 4x² +9y² + z² = 36 b) x² - y²z² = 1 c) x² +100y² - 36z² = 100 d) z = z= 2x² - 4y² e) x = z² - y²…

A: d)

Q: Solve the system of equations by any method. -3x+6y= 27 x - 2y = -9 Enter the exact answer as an…

A:

Q: 8. 9. A) 1−sinx Ĵ (COSX + 1 COS X+X 2(cosx+x)2 E) ·x)³ dx = ? 1+tan²a (2 + tana)² -+C B) +C D)…

A:

Q: Evaluate 3+x lim,¬4¹ (x-4)(x+2) 01 0 0 8-8 O +∞

A: The given limit is: limx→4+3+xx-4x+2

Q: Given the function: f(x) = { // x³-1 x-1 if x #1 k if x = 1 What should be the value of k so that f…

A:

Q: Find the derivative of the following function. Factor fully and simplify your answer so no negative…

A:

Q: A region bounded by f(x) = 5 — x, y = 0, and x = 1 is shown below. Find the volume of the solid…

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Q: 5.2 Consider the curve that passes through the point (0,10) and is such that the slope of the…

A: We have to find the curve that satisfies the given conditions of the problem.

Q: Let f be a function with continuous second partial derivatives and define: z = f (2x³y - y₁y³) if…

A: z= f(2x3y-y,y5) ,  u= 2x3y-y, w= y5   And zy= (2x3-1)fu+5y4fw  Find zyx

Q: A region bounded by f(x) = √√4 — x², y = 0, and x = 0 is shown below. Find the volume of the solid…

A:

Q: 5. Calculate the area between the Curve fex) = 4-x² and y = 4, y = 2x_4? 20 GMS: S-U 3

A: To find the area bounded by the curves f(x)=4-x2, y=4, y=2x-4. The region bounded by the curves is:

Q: Find the net signed area of ƒ (x) = x - 2 over the interval [0, 6], illustrated in the following…

A:

Q: What is the area of a quadrilateral with vertices at (-2,-6), (1,-6), (-2,0), and (1,0)? Enter the…

A:

Q: If f(x) dx = 3 and g(x)dx = −2, then which of the following must be true? I. f(x) > g(x) for all a ≤…

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Q: Suppose a certain drug is administered to a patient, with the percent of concentration of the drug…

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Q: Use tables to determine if x²+x-12 exists. If it exists state the value of the limit. lim x→+3 x-3

A:

Q: a. Use limits to find the derivative function f′ for the function f. b. Evaluate f′(a) for the given…

A: The given function,    fs=5s3+3s, a=-3

Q: Recall that an equation of a circle can be written in standard form (x-h)² + (y-k)² = r, where (h,…

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Q: dy Solve the differential equation dx x6 +4y X

A:

Q: Assume that the random variable X is normally distributed, with mean μ = 70 and standard deviation…

A: To find the probablity P(X>a)  then we have to convert the expression into  Z-score value of the…

Q: 11. Find the angle between the planes: 4y + 3z = -12 and 3x +2y + 6z = 6.

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Q: B)ls w = Ze² analytical function or not?

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Q: dy B)Solve differential equation dx -(x²+y) x+siny

A:

Q: cos(In2x) X A) cos(Inx) + c C) sin(In2x) + c dx = ? B) sin(Inx) + c D) E) 2.sin(In2x) + c 2…

A: Given

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: Draw the graph:-    y=0 ( x-axis)  and y=√(x-x2)

Q: the complex number 6√3+6i in polar form O 12(cos(n/6)+isin(n/6) O 12(cos(n/4)+isin(n/4) O…

A: As we know that; The complex number z=a+ib can be written as polar form; z=rcosθ+isinθ Where;…

Q: Solve the initial value problem y" + y = 0, y(3) = 8, y'(n/3) = − 16 Oy(t) = √√√3cost + 8√/3sint…

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Q: Asymptotic to x= 0, x=5 and y=0

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. X = =…

A:

Q: Find the domain and range of the following function: f (x)  {(2,3),(3,4),(5,7),(10,3)}

A: Given: f (x) = {(2,3),(3,4),(5,7),(10,3)}

Q: For the next three exercises, use power series operations to determine the Maclaurin series for the…

A: Given

Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

A: This question is related to definite integration, we will solve it using given information.

Q: Find an equation of the tangent line to the graph of y = x³ - 3x - 1 at the point (2, 1).

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Q: Refer to functions p and q. Evaluate (qop)(x) and write the domain in interval notation. Write your…

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Q: Prove the limit below exists, by using the Binomial Theorem and the Monotone converge ONLY. Do not…

A: Prove the limit below exists, by using the Binomial Theorem and the Monotone converge ONLY. Do not…

Q: Solve the given differential equation by undetermined coefficients. y" + 2y' + y = sin(x) + 4…

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Q: Since the creation of a social program, the percent of persons 65 years and over with a family…

A: Here we have to us ethe given function.

Q: Evaluate f"(c) at the point. 9) f(x) = In (4x - 3), c = 1 10) f(x)=3x2-3, c=1 3x - 4 11) f(x)= 4x-3'…

A: