Consider the integral 2³ In(a) dz: Applying the integration by parts technique, let u = ln(2) du=z³✓da de Then w - fodu - x Add Work Submit Question and x da

Q: Given the DE as 2xy² + 4 = 2(3-x²y)y'. A. prove or disprove if the given D.E. is exact. B. If it is…

A: The given differential equation 2xy2+4=23-x2yy' Exact differential equation:    The differential…

Q: The graph below is the function f(x) -5 -4 -3 -2 -1 Find lim H-2 5 4 Find f(2) 3 2 1 -1 -2 -3 S 1 2…

A: Solution:

Q: f(x) = 9+x= x + 1 f(x) = f(4) X-4

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Q: 32. ³+x²+x+2 + 1)(x² + 2) dx

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Q: Evaluate the following integral. 40x² x4-52x² +576 dx Find the partial fraction decomposition of the…

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Q: Find the equation of a plane that is perpendicular to the vector 4 i + 2 j - 2 k and passing through…

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Q: Define g(2) for the given function so that it is continuous at x = 2. 2x²-8 2x - 4 g(x)= Define g(2)…

A: We can find the correct answer in the below steps.

Q: of the shaded region. y = x² - - 15 x (-4,-4) 20 10 -10 - 20

A: The equation of the curves are: C1: y = x3-15x C2: y = x The graph of the curves To evaluate: The…

Q: Use integration by parts to evaluate the integral. Round your answer to the nearest tenth. In(z) S²…

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Q: Which of the following is the complete set of roots of the auxiliary equation fory""-3y+3y'-y = 0.

A: Given y'''-3y''+3y'-y=0

Q: The graph of f is shown on the coordinate plane. Selected values for g are shown in the table. Graph…

A: The graph of the function fx is The table for the function gx is

Q: 1. Solve the following initial value problems. (a) y = r cos(1²), y(√) = 1 (b) y" = r², y(0) = 3,…

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Q: Express (5x + 7y, 8x + 5y, 0) as the sum of a curl free vector field and a divergence free vector…

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Q: Transform each graph as specified below. (a) The graph of y=f(x) is shown. Draw the graph of…

A: Solution is given below:

Q: Suppose that a volcano is erupting. Readings of the rate r(t) at which solid mate- rials are spewed…

A: Given data   t 0 1 2 3 4 5 6 r(t) 2 10 24 36 46 54 60

Q: Let f(x, y) = axy + ax²y + y³. (a) div(grad(f)) : = (b) Find a so that div(grad(ƒ)) = 0 for all x,…

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Q: Given s(t)=t² + t, find (a) v(t). (c) the velocity and acceleration when t = 4. (b) a(t). (a) v(t) =…

A: Concept: The instantaneous velocity at a given time is the derivative of a function that represents…

Q: 1) Find the difference quotient of f(x)=x². That is, find f(x+h)-f(x) for h#0. Simplify so h that h…

A: To find the difference quotient of the given function.

Q: Consider the planes given by the equations − (x + 2y + 5z) = 1, - x=y+z= 4. (a) Find a vector…

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Q: Researchers developed a function that can be used to accurately predict the weight of female cows,…

A: Researchers developed a function that can be used to accurately predict the weight of female cows,…

Q: 4 = √² 43 √8-7x8 dx

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Q: mation 9. y'-y = 2te²¹, y(0) = 1 2

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Q: Find P.S. of y (2x²-xy + ²) dx -x ² (2x-1) dy=0 4 = 1/2 when x=/

A: The given Initial value problem is y2x2-xy+y2dx-x22x-1dy=0 when x=1, y=12. Let's check the given…

Q: Write an equation for a rat Vertical asym Enclose numerators and de Include a multiplication sign…

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Q: K For the piecewise function, find the values h(-9), h(1), h(S), and h(7) -5x-9, for x<-3 H() = 5,…

A: Topic - Functions

Q: y=ae³x + be-3; y"-9y=0 -3.x.

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Q: 1. Find the derivatives of the following function (a) y=4²+2

A: Given Equation: y=4x2x-3xx+2xx          .....................(1)y=2x+3x2+x+1…

Q: does the series  E infinity/n=1  2^n/3^n converge or diverge a)the series converges because its is…

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: S 4 ३ 2 मनोर 70 -5 -4 -3 -2 -1 -1 -2 -3- -4- 1-5+ 3 4 (Round all answers to the nearest tenth as…

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Q: Hello, can you help with the below math exercises with the explanation please? Thanks a lot! 5/…

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Q: A shoe company will make a new type of shoe. The fixed cost for the production will be $24,000. The…

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Q: Gratio and proportion diameter of x =…

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Q: Find the roots of an equation f(x)= x^3-x-1 using four iterations of bisection method. Compute also…

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

Q: #4 The function E (t) = 4.66459 t4.4054 describes the available capacity (in kilowatt hours = kWh)…

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Q: Find the decomposition a = ªb + ªь with respect to b if a = (x, y, z), b = (-1,-1,-1). (Give your…

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Q: 3) Prove that : tan z = 올n(부를) In

A: To prove the given identity.

Q: 51. Lim ex-1 хто егу +2ex-3

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Q: Use the following function and its graph to answer (a) through (d) below. 4-X, X2. Let f(x)= a. Find…

A: Given that fx=4-x,x&lt;2x+1,x&gt;2Solution :

Q: Find an equation for the plane through the points (3, 4, 5), (-1, 2, 0), (-2, 0, 2). The plane is

A: Find an equation for the plane trrough the points (3, 4, 5), (-1, 2, 0), (-2, 0, 2) .

Q: 8. Evaluate: lim |5-x| x-5-5-x

A: To evaluate the following limit.limx→5- 5-x5-x

Q: b) Calculate the following definite integral: [*(√x - 3) dx

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Q: 1. Suppose Delta Corp allocates $600,000 to spend on research and marketing. Delta Corp estimates…

A: Suppose Delta Corp allocates $600,000 to spend on research and marketing.Delta Corp estimates that…

Q: The graph of f is shown on the coordinate plane. Selected values for g are shown in the table. Graph…

A: The graph of the function fx is given by The table for the function gx is

Q: Find lim x→-3 sin(−4 π x)   lim x→-3 sin(−4 π x)

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Q: 5T A positive angle less than 47 that is coterminal to 4 Part: 1/2 Part 2 of 2 is 57 A negative…

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Q: YA -3 x (a) If f is increasing on an interval, then the y-values of the points on the graph [rise…

A: Given graph of function is

Q: Express the following functions in the form utiv • f(Z) = ln (1+z) P

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Q: Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line…

A: Greens theorem states that "for closed curve C enclosed a region R then the line integral along the…

Q: 2Y+ 3/4X=Z/3

A: The given expression 2Y+34X=Z3 we have to solve the expression for X,Y and Z