Check the existence and uniqueness of a solution of the following Initial Value Problem: AP (T-A) dx y(2) = 1 =√x²+2y -

Q: Sketch the graph of a function g that satisfies the following conditions: ˆ g(0) = 1, g(2) = −1, and…

A: here,     at x = 0, g(x) = 1;   at x = 2, g(x) = -1;   at x = 3, g(x) = 1;

Q: What is the minimum order of the Taylor polynomial centered at 0 for cos x required to approximate…

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Q: 29-34 Evaluate the integral by interpreting it in terms of areas. 29. f (x - 1) dx 30. 2₂ √4 - x² dx…

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Q: Find S- (x² + 4) ³. 43 dx

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Q: Consider the vector field F = Evaluate r(t) = t²i+t³j, 0≤ t ≤ 2 LE F-dr along the curve C:

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Q: 36. Given that 3x√x² + 4 dx = 5√5 – 8, what is S₁3u √/u² + 4 du?

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Q: Consider the functions f(x)=8arcsin(52) g(r)=16arctan (a) Find the derivatives of f(x) and g(x).…

A: This topic is related to inverse trignometric relation and their derivative.

Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 16П3 1 3 a 09 16П3 1 2п 3 (82)³/ (8r-2)3/2 3√8

A: a2=a

Q: many different 8-digit phone numbers do not contain the digit 4? Assume that any digit in the phone…

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Q: Find the surface area of the part of the plane z7+ 4+ 5y that lies inside the cylinder 16 Calculator

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Q: Compute the flux of the vector field (³, - xy), out of the rectangle with vertices (0,0), (5,0),…

A: The flux of the vector field x3,-xy5 Graph

Q: 1 1) Find the Taylor Series for - X about a = 1

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Q: a laluale exactly arcsin 2 There are Two answers from 0° to 360°) arc Cos

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Q: Consider the vector field F= ·1.² F-dr along the curve C: F(t) = 4 con(t)i + 4 sin(t)), 0≤1≤…

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Q: Find the Jacobian of the transformation. x = 8e³+, y = 6e³-t a(x, y) à(s, t) =

A: To find the Jacobian of the following transformation. x=8es+t, y=6es-t

Q: Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region…

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Q: Find​ E(x), ​E(x^2​), the​ mean, the standard deviation and​ variance, over the given​ interval, of…

A: The probability density function and the interval is given below               fx=113…

Q: Find all solutions of the equation in the interval [0°, 360°). (Enter your answers from smallest to…

A: To solve the following

Q: A person's metabolic rate tends to go up after eating a meal and then, after some time has passed,…

A: NOTE: Refresh your page if you can't see any equations. . the thermic effect on food for one…

Q: x² - 8x + 12 2 .2 x² - 4x

A: Given,

Q: about the y Find the volume of the solid obtained by rotating the bounded region determined by the…

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Q: y" - 4y' = -4te²t, y(0) = 0, y'(0) = 1

A: Differential equation is called the equation which contains the unknown function and its derivatives…

Q: Find the mass and the indicated coordinates of the center of mass of the solid region Q of density p…

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Q: Below is the graph of the function f(x). M On what intervals is f(x) concave down? -1.5 1.5 x 0.5…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 8 (3x)" Σ n = on + 4 n+4

A: Summation of (3x) n/(n+4), n from 0 to infinity.

Q: 1/3 Given the curve xy¹/³ +y = 10, find the slope of the tangent line at the point (1,8). [C] 25 [A]…

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Q: Part II. Using a computer graphing calculator software (state what did you use), construct an…

A: Given the data of population growth of a region. It is required to find the model for the population…

Q: Find the area between the following curves. x= -3, x= 3, y=e*, and y = 5-e*

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Q: 5.) Determine the convergence or divergence of the series Σ n(" + ¹) n n=1

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Q: 7. y" - 4y = 3e¯t, y(0) = 1, y'(0) = = −3

A: Given: y''-4y=3e-t,y(0)=1,y'(0)=-3 The objective is to find the solution to the given initial value…

Q: 21. Please express sin(t³) dx as a limit of right regular Riemann sums. a. Ax= b. Xk =

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. x + 8x+16 D. 2 X 2 X…

A: I=∫x3x2+8x+16dx

Q: ps) Find the degree 3 Taylor polynomial T3(x) of the function f(x) = (3x − 4)4/³ at a = 4. T3(x) = =

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Q: (12) Solve for X 12 % X 10

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Q: 1. Let F(x, y, z) be the vector field (z, 2x, 2y) and C be the curve parameterized by r(t) =…

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Q: Find the curl of the vector field F = curl F = i + j+ 16 k

A: To find the curl of vector F, F→=<yx5,xz6,zy2>

Q: Find the unique solution of the second-order initial value problem. y"-y'-6y= 0, y(0)=2, y'(0)=11

A: Given- y"-y'-6y=0 and the boundary condition is y0=2 and y'0=11. To find- The unique solution of…

Q: Evaluate zy³dz + zªdy, where C is the rectangle with vertices (0,0), (6,0), (6,2), and (0,2)…

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Q: (12) The point (2, 3) is on the unit circle in second quadrant. Find the x-coordinate of this point.

A: We have to find the x-coordinate of the given point. For this we will use Pythagorean theorem.

Q: Let lim f(x) = 8 and lim g(x) = 6. Use the limit rules to find the following limit. x-2 X-2 lim X-2…

A: given, limx→2f(x)=8  and limx→2g(x)=6let   B=limx→2f(x)+g(x)4g(x)

Q: What is the formula for each step of Euler's method, for the differential equation Dy/dx=f(x,y)

A: Euler's method is a numerical method for approximating the solution of a first-order ordinary…

Q: f(0) = {! 0 2≤1≤3 otherwise. Find the Laplace transform F(s) by computing the following integ 1.…

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Q: Evaluate F. dr along each path. (Hint: If F is conservative, the integration may be easier on an…

A: Fx,y,z=yzi+xzj+xyk

Q: 10.y" + 2y' +10y = -6e-t sin(3t), y(0) = 0, y'(0) = 1

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(9, 3,…

A: We have to show if the given points are of parallelogram and find its area. For this firs we will…

Q: A particle is traveling in a straight line. Its position at time t in seconds is given by s(t) = 4√t…

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Q: Graph the sets of points whose polar coordinates satisfy the inequality. r27 Choose the graph that…

A: To graph: The polar inequality r≥7.

Q: Find the indefinite integral and check the result by differentiating. S(3x+10)*(3)dx [(3x +…

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Q: Anthony rides a train along a straight north-south track. His position at time ₺ in hour is s(t) =…

A: Let position function denoted by s( t ) Let velocity function denotes by v( t ) Average velocity…