Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (7x²2) to evaluate the integral 0.61 sin (72²) dz 0 Your answer will be an infinite series. Use the first two terms to estimate its value.

Q: Determine the equations of the tangent and normal to the curve y=2xex at (0,0)

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Q: 412 Evaluate the integral (x² + y² + z²) dz dy dx. SSS 000 412 SS S (x² + y² + z²) dz dy dx = [ 000…

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Q: H.W: Sketch the following functions 1. x² + y² = z + 1 2. x² + y² + 2y + 1+ 2+ z = 0 3. z² = x² -…

A: In these question , we can sketch the given function . Note : As per our Guidelines , we can solve…

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Q: 7. f(x) == 8. f(x) = |x| |x|+1

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Q: Convert x = = ln(2t) and y = 1² from parametric to rectangular form. 2

A: Given,  x=ln(2t) and y=12t2

Q: 5) Calculate the area in square units, bounded by g(x)= 4x+8_and_f(x)=x² +19x+62 over the interval…

A: NOTE: Refresh your page if you can't see any equations. . here we have  and the interval is  so…

Q: J; x² x² - 1 4 dx

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Q: Find the exact coordinates of the centroid for the region bounded by the curves y = 4-2² and y = 0.…

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Q: The function 5x+1 f(x) 1-In (x³ +e) has a Maclaurin Expansion O false O true

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Q: Assume that the vectors a, b, c, and d are defined as follows: a = (8,3) b = (6,5) c = (4, -1) d…

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Q: Let the vector v have an initial point at (2, −8) and a terminal point at (−1, −8). Determine the…

A: Let the vector v have an initial point at 2, -8 and a terminal point at -1, -8.To determine the…

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Q: Find the vertical asymptote of the graph of f(x) Describe the behavior of f(x) to the left and right…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Find the eigenvalues ₁ < ₂ and associated unit eigenvectors A = 16 -8 -8 4 The smaller eigenvalue ₁…

A: We can solve this as follows:

Q: dy Use Picard's method to solve =-xy, y (0) = 1 dx Find y3(1)?

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Q: What is the component form of the position vector for a vector with an initial point of (-1,0) and a…

A: We have to find component form of position vector.

Q: Determine the equation of the ellipse with foci (1, 4) and (-5, 4), and co-vertices (-2,8) and…

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Q: Evaluate the spherical coordinate integral. 1- cos 2 2π π SS S p²sin & dp do de 00 0

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(In(5t)) dt t

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Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

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Q: Compute the area of the region enclosed x² 5x X 1) y 2 2 2 +

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Q: Evaluate the integral. 1³w² in w² In(w) dw

A: We will solve the integration

Q: Let C be any curve from (0, 0, 0) to (4, 7, 2) and define a vector field F(x, y, z) = (y cos xy, x…

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Q: 3. Reverse the order of integration in 24e² dydx and then evaluate the integral with the new limits

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Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. Use Lagrange…

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Q: P-4 Use separation of variables to find the product solution of the following a) ди ди b) J2u 02u y…

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Q: 2. Below is a graph of the exponential function f(x)=2¹. 10- 9. -10-9-8 10 +6 a. Describe in words…

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Q: ectors u = (−8, 1) and v = (-7,-8), find the difference v- at the difference graphically in two…

A: Here I am providing my handwritten solution

Q: 2 cosh x +losion2x = 5

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

Q: Find the marginal profit function if cost and revenue are Pix- given by C(x)=215 +0.7x and R(x) = 3x…

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Q: Find all the values of x such that the given series would converge. 8 3n (x2)(n+1) (n + 5) n=1 The…

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Q: For which of the following does the Mean Value Theorem apply? TT a) f(x) = tanx, - ≤x≤I b) f(x) =…

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Q: 6e at x-b First find where the two curves meet. y = 5e" meets y = 6e where b Then Area = - f(x) dx…

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Q: x²y" + 2xy' 6y = 0 -

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Q: Determine the equation of the hyperbola with center (−1, –4), a focus at (−11, –4), and a vertex at…

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Q: A tank in the shape of an inverted right circular cone has height 7 meters and radius 2 meters. It…

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Q: Determine the equation of the ellipse with center (-2,-4), a focus at (-2,5), and a co-vertex at…

A: Given:        center =-2,-4        focus =-2,5        co-vertex 10,-4 Equation of Ellipse is…

Q: (d) √ ² (3 (3 − z)(3z + 1) dz. 0

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Q: Evaluate the iterated integral. 14 Sxy ex dy dx 03 14 SSxy ex dy dx = [ 03 (Type an exact answer in…

A: Topic = Integration

Q: the amplitude is the only incorrect answer

A: Solution :- By compare standard cosine function y= Acos(Bx-C)+D

Q: the sum if convergent. 4) 2-6+18-54...

A: In this question, we will evaluate this series and test for convergence.

Q: 21. Jo 0 dx (x + 1)(x² + 1)

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Q: x+1 2-1 24 - 1 Evaluate the given limit of lim O-1 01/1 0 -¹ O Olimit does not exist if it exists.

A: Solved below...

Q: Find f(x) by solving the initial value problem. 5 f'(x) = 2x + 5ex + —; X f(x) = f(1) = 6 + 5e

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Q: 1) Solve the initial value problem. Show All Your Work. dy 2x+sec² X 2y , y(0) = -5. dx

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=2 ex cos (yz), Po(0,0,0),…

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Q: Given plane z: 3x+2y+=-3=0, point P(1, -2, 3), and lines 1₁:¹¹ and 4₂: (3, 6,-5)+r(2, 3, 1), find:…

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Q: Evaluate the integral. (Use C for the constant of integration.) ] = 5 tan(x) sec³(x) dx

A: The given integration is: ∫5tanxsec3xdx To find the value of integration.