Find the decomposition a = ab + ab with respect to b if a = (x, y, z), b = (1, 1,−1).

Q: 10. For f(x) = xe-x², a. Give in interval notation the intervals where f is increasing and where fis…

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Q: 3. (4.2 #3) Find the general solution. y" + 8y + 7y=0

A: The given equation is; y''+8y'+7y=0

Q: .Jeremy bought x pounds of peanuts for $4.50 per pound and y pounds of cashews for $7.05 per pound…

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Q: 3.) Find the area of the region bounded by the graphs of y = x - 1, y = -x + 3, and x = -1.

A: Region bounded by the graphs ofy=x−1,y=−x+3, and x=−1.

Q: 1₁ 4 tan x sec x dx I

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Q: Line 1 is defined by slope m = 3 and y-intercept (0, −2). Line 2 passes through the point (3, 5) and…

A: Line 1 is defined by slope m = 3 and y-intercept (0, −2). Line 2 passes through the point (3, 5) and…

Q: 19-26. Evaluating limits graphically Sketch a graph of f and use it to make a conjecture about the…

A: We say that the limit of a function f(x) exists at a point x=a if the value of f(x) approaches same…

Q: Suppose f is differentiable and that Select one: O a. 9 S." O b. 27 O c. 1 O d. 3 3 f(u) du 9. Find…

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Q: Let F= LF C Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (1,0,0),…

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Q: Suppose that the function fis defined for all real numbers as follows. -10+xif -4<x<4 x24 √(x) =…

A: Drawing the graph of the function for

Q: ро b) Point P (3, 7) is in coordinate. Express this point in cartésion coordinate

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Q: 7. Evaluate the integral 3x+2 √1-x² dx.

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Q: The graph of y= f(t)dt, where f is a piecewise constant function, is shown here. (a) Over which…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 24. Find the equation of the plane that contains the points (5, 0, 4), (1, 3, 3), and (3, 1,3).

A: Given dataPoints of a plane,

Q: Find the derivative of 27e-5t. O-135e5t O 5e-3/5t O 15e-5t O-5e-5/3t e-5/3t

A: The given function is (27e-5t)1/3

Q: The figure shows the velocity function for motion along a line. Assume the motion begins with an…

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Q: Convert the Cartesian coordinate (-6, 2) to polar coordinates, with 0 ≤ 0 0 r = 2√10 = 1.89 X

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Q: 2-54. Consider a home you purchase for $600, 000, at a down payment of 15% and at a rate of 4.5%.…

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Q: (d) What is the maximum value of f? The maximum value is (e) What is the minimum value of f? The…

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Q: Solve the initial value problem: 10x - 2y√x² +1 dy dx = 0, y(0) = -8

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Q: Find an equation of the tangent line to the curve at the given point. y = 3x³ x² + 2, (1,4) y =

A: Using application of derivatives, we can find slope of tangent and thus it's equation.

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y = 0, y = 9+x⁹…

A: Volume of solid obtained by revolving the region about x axis is given as followsGiven functions

Q: Find the area of the region enclosed by the parabola y = 2 - x² and the line y = -x.

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Q: Solve f6x sin(x) dx using Integration by Parts. 6x and v' = sin(x). Use u =

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Q: Compute the Wronskian of a set of functions W(x) {y₁, y2} = {e cos (√x), eª sin(√x)}

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Q: C. Simplify after removing all symbols in grouping 3x-[(7y-5(8x-2y+32)-11x)-6y-z] 16.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

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Q: Solve fxª ln(x) dx using Integration by Parts. X Use u = = ln(x) and v' = xª. Answer: ID

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Q: 5. Explain how you would use the limit comparison test to determine if the following series is…

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Q: -8 1 −1 (63) −1 2 ?

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2 4 -1 -2] whatever size you like. 3-16. If A = " find a non-zero matrix B such AB = 0, where 0 is a…

A: The given matrix is; A=[2 4     -1 -2]AB=0Find the matrix B.

Q: ex-1 b.) lim x¹ x-0 x²

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Q: 3-4. Consider the linear system x + y = z = 10 -x + y - 11z = 2 2x + 4y + (8 + a)z = 50 (a) Find the…

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Q: Consider the initial value problem y" + 25y = 2 cos(5t), y(0) = 0, y (0) = 0. a. Take the Laplace…

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Q: why is the derivative of (sin(bx)ln(a)) = (ln(a)cos(bx)b)? why is ln(a) treated as a constant?

A: We have the following expression:sin⁡(bx)ln⁡(a)Here x is the variable and a,b are constants

Q: Consider the function Evaluate the definite integral. f(x) = Jx if x < 1 if x ≥ 1 [ f(x) f(x) dx

A: To find the integral

Q: Use the method of reduction of order to find a second solution ty"—(4t − 2)y'+(4t − 4)y=0, t> 0 2t…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: The region bounded by curves Graph of region

Q: Compute the indefinite integral S 2dx x(lnx)2 ab sin (a) 2dx S x (In x)² 8 f дг 8 E ESH

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Q: Evaluate the following definite integral. Your answer must be exact. S cos(arctan(10t)) 1+ (10t)² 5…

A: The given integral is .The aim is to find the value of the integral.

Q: What hap f(n

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Q: solve f(x)= x^3-8/4(x-2)

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Q: Compute the definite integral π/4 x² sin(2x) dx = Cπ/4 x² sin(2x) dx. Enter exact values only help…

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Q: Find a particular solution of Yp(x): y"-2y+y = e(2 – 12x) -

A: Given differential equation is In the given equation,  includes .Consider .To duplicate, multiply…

Q: 4. Explain how you would use the integral test to determine if the following series is convergent or…

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Q: Find the total area of the region between the x-axis and the graph of y=-x²-3x, -7≤x≤1. The total…

A: To find the total area between the region?

Q: Find a formula for the described function. A rectangle has area 9 m². Express the perimeter of the…

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Q: n=1 n2x2n 22η find the interval of convergence.

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Q: 6. Explain how you would use the absolute convergence theorem to show the following series is…

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Q: = GRAPHS AND FUNCTIONS Composition of two functions: Basic Suppose that the functions u and w are…

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