Differentiate the following function: f'(x) = f(x) = e" + ce 니

Q: Find the centroid (x, y) of the triangle with vertices at (0, 0), (10, 0), and (0, 2). 18 15 X=

A: Consider a triangle with vertices at (0,0),(10,0) and (0,2)

Q: Consider the following function. f(x) = 4x² - 7x² Determine whether the function is even, odd, or…

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Q: t Let f(x) = 4x4 + 6. (a) Use the limit process to find the slope of the line tangent to the graph…

A: NOTE: Refresh your page if you can't see any equations. . the given value is x=4 the point on…

Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

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Q: Find the equation of the tangent line to the curve at the given point. \\ y = 1 + 2x − x³, (1, 2) y…

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Q: Sketch the region R and evaluate the iterated integral -1.0 O [²L²¹²- -0.5 (12x+8y) dy dx y 3 £₁ […

A: We can evaluate the given integral by using the integral formulas.

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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

Q: Examine the function for relative extrema and saddle points. (Order your answers from smallest to…

A: The answer as follows:

Q: Part 2 of 8 The equation x³y-x-9y=0 is in the form of ax² + bx+c = 0. The solution set for x is…

A: Let's solve given equation.

Q: Sketch the solid region whose volume is given by the iterated integral. [³ O √,2-4 Evaluate the…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: b y' = 2 + ₁e-ax a

A: details steps are given in step 2

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: 3X y 2y = 4y + 8y = 2³x + 8x² 2X <-2X Ans: y = ₁2x + ₂xe + cze -25 X -3X 2 —=== ² + x + x + 1²/2

A: This is a problem related to ODE. Based on the general formula and concept we will answer.

Q: 23. Express each of the following as a logarithm. Use a calculator to evaluate your answer correct…

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Q: Find three positive numbers whose sum is 114 and whose product is a maximum.

A: follow the procedure given below.

Q: Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

A: The given surface is zex^2-y^2-1=0 and point (6,6,1).

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: Evaluate the iterated integral. ITT 4ze dy dx dz

A: ∫14∫01∫0x34ze-x4dydxdz

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

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Q: A textbook company publishes computer, educational and utility type of books. Their business…

A: We have to find how many educational books should the company publish annually for maximum profit.

Q: Calculate the exact slope m (rather than a decimal approximation) of the straight line through the…

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Q: Solve the following ODES by Undetermined Coeff. X X A 1 3X 2 • Y -2y = 4y + 8y = 2³x + 8x² - + 2X -…

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Q: Given the unit circle, x^2 +y^2=1. Sketch the unit circle and pick a point K(a,b) on the unit circle…

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Q: Find three positive numbers x, y, and z that satisfy the given conditions. The sum is 40 and P =…

A: Given that    Three positive numbers x,y and z                The sum of these numbers is 40.…

Q: Write an equation for the function graphed below 4 y = 3+ 2+ 1 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3- -4 -5+…

A: topic- equation of a function

Q: A) Let g(x) (5x+24 =x² 2x+8 x<-3 -3<x<4 x 24 a) lim g(x), lim g(x) X--3 evaluate the following…

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Q: USE NEWTON-RAPHSON'S METHOD IN FINDING ROOTS f(x) = ex²-2 + √√x + 2-3

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Q: Umm can this be answered more clearer, I can't really tell what the answer is, and when I put it in…

A: Let's solve.

Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

A: Topic = Application of Derivative

Q: Find all solutions of the equation 4 cos(3θ + π/4)+2=0 in the interval [0,2π].

A: Solution of given question is written in below steps.

Q: State the range of f(x)= {v=Ry>} b. ve Rly - } 3 a. 1 3x+4 C. {v=Ry>0} d. {ve Rly 0}

A: We can find the range as below.

Q: Which of the following is a power series representation of f(x) f(x) = Σ(-1)". n=0 8 x2n f(x) = Σ 16…

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Q: 7. Determine the intersection, if any, of the planes with equations x +y-z + 12 =0 and 2x + 4y - 3z…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first first question.…

Q: Evaluate the iterated integral. •π/2 [y/6 [5/y } 0 sin y dz dx dy

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Q: (4x²y² - x² + 4xy² - x) dx + (2xy + x + 2y + 1)dy = 0

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Q: 6. Evaluate the following real integrals by residue theorem 3 T 211 I- -S do coso + 2 sing +3 ans o…

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Q: Solve the following ODES by Undetermined Coeff 11 4X y - 16 y = 19,2 € + 60e, y(a) = Y(u). 4X -4X…

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Q: Find the determinant. x² -Ed 2x 5x4 W(x5, x²) = = (x²)(5x4) - (2x)(x5) The Wronskian ---Select---…

A: We need to fill in the blanks.

Q: Evaluate the integral. (Use C for the constant of integration.) tan(x) cos(x) dx

A: ∫tan8xcos9xdx

Q: 5. Use an iterated integral to find the volume of the solid that is bounded above by the plane…

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Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A: We need to fill in the blanks.

Q: 2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

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Q: A swimming pool whose volume is 10,000 gal contains water that is 0.03% chlorine. Starting at t=0,…

A: Given: the volume of swimming pool = 10000 gal that contains 0.03% chlorine. at t=0  ,0.002%…

Q: Find the area of the region bounded by the parabola y^2=x+3 and the line x - y = -1

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 12e - 3 y(x) =

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Q: Consider the following function. f(x) = x¹/⁹ + 5 (a) Find the critical numbers of f. (Enter your…

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Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.…

A: increasing and decreasing intervals of fucntion  fx=3x4 − 4x3 − 12x2 + 5

Q: 4. In a chemistry class, the students in a lab derived a function to model the results of their…

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