Use the Fundamental Theorem of Calculus to find the "area under curve" of -x² + 8x between x = 1 and x = 5. In your calculations, if you need to round, do not do so until the very end of the problem.

Q: find all possible functions with the given derivatives  y'=7x6+9

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Q: 00 Determine whether the alternating series (-1)+1 √n +9 n+7 n=1 converges or diverges. (...) Choose…

A: Consider the series

Q: For the following function, a) give the coordinates of any critical points and classify each point…

A: Consider the function

Q: If a 5, b= 7, and c= 11, find the measure of ZC. ZC b C • Enter your answer as a decimal value. •…

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Q: The augmented matrix of a system of linear equations is given in reduced row-echelon form. Find the…

A: To find the solution of the following system.

Q: Find an equation for the hyperbola described below. Graph the equation by hand. Vertices at (0, -8)…

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Q: Find the maximum rate of change of f(s, t) - test at the point (0,-5). Answer:

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Q: Find a basis for the 2-dimensional solution space of the given differential equation: y" - 5y' = 0

A: The given differential equation is

Q: Suppose R is the solid bounded by the plane z = 2x, the surface z = 2, and the planes y = 0 and y =…

A: R is solid bounded by the plane z = 2x, the surface z = x2  and the plane y = 0 and y = 3. Find…

Q: Please help me with #2 and #3, too. I will give rate for both

A: Question No. (2):To find the inverse Laplace transform.Note:  Since, the student has has mentioned…

Q: standard y = mx + b form, the tangent line to the parametric curve( 1/(t^2 +1) , 1/t) at the

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Q: Find the divF given that F=∇f=∇ where f(x,y,z)=xy^3z^2 divF=

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Q: The manager of a 100-unit apartment complex knows from experience that all units will be occupied if…

A: Given Information - If the rent is $700 then all 100-unit apartments of the complex will be…

Q: Let T be a linear transformation induced by the matrix A = Find the matrix of T-¹.

A: The given matrix is,A=(4−32−2)Find the determinant of the matrix…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = (y² + 2)³/2,…

A: The area of the surface of revolution of  rotated about the x-axis on  is:

Q: Suppose sin(theta) = 3\5 and theta in quadrant 2. Find the exact value of the following. Solve with…

A: Given:, where   is in 2nd quadrant.To find:To find the exact value of the following.Note: Since, the…

Q: Both first partial derivatives of the function f(x,y) are zero at the given point. Use the…

A: given function

Q: 2 K A clothing company determines that its marginal cost, in dollars per dress, is given by the…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Given that the region bounded by the curves

Q: 9. Find and simplify the difference quotient for a. g(x) = 2²/12 X b. f(x) = √x

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Q: Find the antiderivative F off that satisfies the given condition. Check your answer by comparing the…

A: The function is given byTo determine: The expression of antiderivative .

Q: Evaluate the following integral in cylindrical coordinates. 379-x- 4 jjj 1 -3 0 01+x^+ 3√√9-x² 4 -dz…

A: The given integral is

Q: Suppose that the total cost (in dollars) for a product is g C(x) = 1200+ 190 ln (3x + 1) where x is…

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Q: Use integration by parts to evaluate the integral: fe-t sin( e-tsin(-10t)dt 1 - [ 101 sin(-10t) +…

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Q: 23. Copy and complete the following table of function values. If the function is undefine at a given…

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Q: Solve the equations below exactly. Give your answers in radians, and find all possible values for t…

A: to solve the given trigonometric equations for twhere

Q: Evaluate the following definite integral. Jo 0 F|+ ㅠ 4 3 sin x + 2 cos xd

A: The Sum Rule:The Constant Coefficient Rule:, where is the constant.And use the common integrals:

Q: Graph the functions in Exercises below. What is the period of each function? 32. sin 2x 33. сos TX…

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Q: vehicle is driven 30,000 miles per year, and the annual insurance premium is $1,250, what is the…

A: a vehicle is driven 30,000 miles per year, and the annual insurance premium is $1,250, to find  the…

Q: please provide the answer for part d)

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Q: Find f. (Use C for the constant of the first antiderivative and D for the constant of the second…

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Q: *The purchasing power P of a $20,000 per year pension after t years of 6% inflation can be nodeled…

A: The purchasing power P of a $20,000 per year pension after t years of 6% inflation can be modeled by…

Q: You are building a closed wooden shed in the shape of a rectangular box with a square base. The shed…

A: You are building a closed wooden shed in the shape of a rectangular box witha square base. The shed…

Q: 2. *Write the integral with the order of integration reversed: SS ey 2 L In(x) I W So (2) dardy=…

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Q: Problem Given that the graph of f(x) passes through the point (0, -3) and that the slope of its…

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Q: Suppose we wish to represent the volume of the solid blob B depicted below with a triple integral. 근…

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Q: Use symmetry to evaluate the following 12. 1200 2x³ 2x5 dx

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Q: sketch the graph of (x^2)-(y^2)-(z^2) = 1

A: Consider the equation

Q: b) Which is larger, g(-4) or g(-3) ? Give a eason for your answer. (... c) What is the absolute…

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Q: 1. The value of a parcel of land bought for speculation is increasing according to the formula t1/4…

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Q: Find the average value of the function f on the interval [1, 4], where f(x) = 2x² + 1 X

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Q: Caffeine occurs naturally in a variety of food products such as coffee, tea, and chocolate. The…

A: Caffeine occurs naturally in a variety of food products such as coffee, tea, and chocolate. The…

Q: Find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f. f(x)=x²-12x+4…

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Q: Differentiate the following function. f(x) = -8+4x+9e*

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Q: Substitution in the Definite Integral S Suppose we want to evaluate the definite integral, H -6…

A: ∫3 5 (- 6) / (9x + 6) 2 dxWe make the substitution u = 9x + 6 As beforedu = (du/dx) dxAnd so, with u…

Q: g(b) Use the Substitution Formula, f(g(x))•g'(x) dx = [f(g(x))• g'(x) dx = a. a. 3 S - 3 3 Š - 3 10r…

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Q: Velocity v (mi/h) 150 100 50 t = Acceleration = 4812 Time t (s) Round the answers to the nearest…

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Q: Solve the following inequality. Write the answer in interval notation. 9x - 4 x + 2 ≤-5x

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Q: 1. The diagram below shows the function f(x) drawn to scale. 10 4 -3 -2 1 -1 8 6 4 2 -2 -4 -6 0 1 3…

A: Note:As per our guidelines we are supposed to answer only first 3 subparts.If  if there are multiple…

Q: Suppose F(3) = 5, F(6)= −5, and F(x) -5, and F'(x) = f(x). f§ 4 ƒ ( x ) d x =

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