5. r(x, y) = ln (x + y)

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial…

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Q: Use mathematical induction to prove the following: 1 + 3 + 5 + ... + (2n – 1) = n² for n ≥ 1

A: This question can be solved using the four basic steps of mathematical induction.

Q: 5- ABCD is a trapezoid whose diagonals AC and BD intersect at the point E. If AB=2/3 DC, prove that…

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Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+ 32)sin(t)dt

A: We have to evaluate the given integral.

Q: 3 *+ 3 2- 1 نها 1 2 3 To find the blue shaded area above, we would calculate: [ f(x) de f(x) dx =…

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Q: Q14) [2x (1+x²) x-(1-x²) (1+x²) +CB)- 10 (1+x¹) (1+x²) (1+x²)" (1+x²)" 11 +00) +CD) 11 10 12 1.1…

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Q: The position of a particle moving along a straight line is given by the function S(t) = 2sint +…

A: st=2sint + cos2t   ,where scm , tsect∈0,2π------------------------To find:    Basic information:…

Q: 8. Scoth 2x In (sinh 2x) dx

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Q: Consider the function f(x) = 4sin(pi/3(x-2) + 8  what is the maximum and minimum y values and their…

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Q: 2 =(x² - 1)³/²,1 ≤ x ≤ 3

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Q: y = 1 x=y² B A (0,0) y=x² C (1, 1) X=1 X

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Q: Find the equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤…

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Q: (a) Find if x² + y² + xy =1 dy dx (b) Identify the nature of the stationary points of y=4x³ - 21x²…

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Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: H.W: Evaluate the integral 30 1. [[(x²y = 2xy)dydx 0 (2x- - y)dydx 2m [[(sinx+cosy)dxdy 3. 5. 2. (x…

A: Since you have posted a question with multiple sub parts, we will solve the first three subparts for…

Q: Consider the right triangle shown below where a = 7.02, b = 11.18, and c = 13.2. Note that and are…

A: Given, a=7.02,b=11.18c=13.2

Q: B. Solve the following integrals. 1.) ²(x + 1)dydx

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Q: 1 (2m-3)√4m (m-3) dm

A: Given

Q: Solve the given differential equation by using separable variables. 2. dy y-1 = dx x + 3

A: We will solve the given differetial equation using separation of variables.

Q: Calculate the Taylor polynomials T₂(x) and T3(x) centered at a = 10 for f(x) = ln(x + 1).

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Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

A: Given.

Q: Find the derivative of the following functions by using the limit definition of the derivative.…

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Q: Use Taylor's Theorem to find an interval [ z, z] where the Maclaurin polynomial p2(x) = 1- 2 1…

A: Given problem  is :

Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

A: Let's find volume of solid.

Q: Identify the surfaces of equations in the Cartesian form. Show your complete solutions. (a) 2² = 4 +…

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Q: Use the Product Rule to find the derivative of the function. f(x) = 9ex cos x

A: product rule: (uv)' = u'v+uv'

Q: H.W Find the taylor series of the following functions for the given points:- 1- f(x)= ln x a = 2

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Q: 49 - x² Evaluate the integral: dx 8x² (A) Which trig substitution is correct for this integral? x =…

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Q: seconds after the start of the movement. (B) Use Tabular integration to evaluate the following: -…

A: Let's evaluate given integral by using tabular method.

Q: 1. Find the limit, if it exists. If the limit does not exist, explain why. 8x³+2x+1+x+2 (b) lim 5x +…

A: Solution: The objective is to find the given limit

Q: Let f(x)=sinx. Determine the x-value(s) where the function has a maximum or minimum value on 0,2m).…

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Q: (c) an = (-1)". 2n n!

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Q: 2 Sketch the graph of each function for 0≤x≤27. a y=-sin x by=-2 sinx c y=-3 sinx d Explain to a…

A: 2. a.)  The graph of y = - sinx  is

Q: For the function z = 3x³5x³y² + 4y³, Show that Zyx = Zxy

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Q: Determine whether the given function is even, or odd, or neither. One period is defined for the…

A: Odd function        f(x) = -f(x)     for all xEven function        f(x) = f(x)     for all xIf…

Q: y = 1 (1,1) A X=1 y=x² C X (0,0) Region A is bounded by the parabola x = y², the line y = 1, and the…

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Q: 80 80 (20) If the graph of the function f(x) is stretched vertically by a factor 2 and then…

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Q: Let f be the function below. You can click on the graph to get a larger image. M Determine the…

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Q: Find the volume of a pyramid with height 19 and rectangular base with dimensions 4 and 11 using…

A: Let's find volume by integration.

Q: 4) Angle A of triangle ABC is decreasing at the rate of 4 degrees per second, while sides AB and AC…

A: According to the guidelines if we get more then one question then we have to solve only first…

Q: What value of x is paired to y=15 using the function f(x) = 2x²-3x+1? none of the choices O-2 3 2

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

Q: $500 at 5% compound continusouly for 11 years. Round to the nearest cent

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Q: 4.2 Given g(x) = ) = cos z + sin for 0 <<, find the value of f(x + 1)dg(x). END

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Q: differentiate 3thetacos(2theta)+2sin(2theta)

A: A detailed solution is given below.

Q: Evaluate the following. Show your complete solution. 1. S. 2³ dz ₂ S. 39 dy 3/4 2. 6 S. 3. dx S.…

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Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: What is the general formula for the nth term of the sequence –4, 1, 8, 17, 28, ...?

A: To determine the general formula for the nth term of the following sequence.  –4, 1, 8, 17, 28, ...…

Q: Calculate the value of the line integral fds where f(x, y, z)=e² and C is described by X C (x, y,…

A: The objective of the question is evaluate the definite integral.

Q: Show tha

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Q: A: f'(√) = -2. B: f'(√) = -1. C: f'(√) = √√. D: f'(√) = 1. E: f'(√) = 2. If fr. 70 f(t) dt =…

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