Q1. Find the homogeneous and particular solutions for the given D.E using the undetermined coefficients method y" + y = tet

Q: 6. Derive the reduction formula for f q²dq (a²+q²)m

A: Using substitution find the reduction in trigonometry function

Q: Find a number in [0,1] such that the difference of 1/3 the number from its cube is minimized.…

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Q: 2x³ is an antiderivative of what function? y = 6x² y = -6x² X y = y = - 2 X 2

A: 2x3 is an antiderivative of what function.

Q: For the next three series, (a) determine the radius of convergence, (b) determine for which the…

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Q: 3. Consider the vectors X and Y in R³ where X = i +3j and Y = 4i - 2j+2k. Find the unit vector…

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Q: lim cos x x-0 , which among the following should result, in equivalent form, before L'Hopital's Rule…

A: To evaluate: limx→0 cosxx Let y= limx→0 cosxx ⇒y= limx→0 cosx1x

Q: Given f(x)=√ and g(x) = x. Which of the following integrals describes the area between the curves…

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Q: please answer #2 #3 #4 find the transcendental curve sketching and the following a. symmetry b.…

A: Since we are given the multiple number of questions and answered according to the guidelines.

Q: 10 5(5+10) a/n A ナ B 5+10

A: See the details solution in below

Q: The 7th derivative of ƒ(x) = 3ñx³ – 12x4 + 7x³ − 11x² + √5 with respect to a is

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Q: How. Find the lengths for the following curver. 7 \- r = 1 + cosa

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

Q: dx X २ Assume that x and I are differentiable functions of t, and 3xx -x ³² + y² = @ 3 Find dx (xc)…

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Q: 29 ² (²4) is the derivative of a function g(x). Over which one of the following intervals is the…

A: Given :g'(x)=x2x2-4x2+1

Q: limit. Determine whether the sequence converges or diverges. If it converges, find the 3n + 5 an =…

A: Given.

Q: What is the lim (3)¯ I 7 sec (7x) cos(3x)?

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Q: Give the general equation of the plane containing the point (3,-1,4) and 2-2 -3 4. | perpendicular…

A: given plane pass through the point(3,-1,4)

Q: Which of the following is TRUE for all? All functions are continuous at all points in its domain.…

A: Given :   Continous and differentiable functions

Q: Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

A: Given: f(x)=ln3-2x,a=1

Q: Determine the area bounded by y = x³ and y = 4x using a vertical element

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Q: 1. Determine whether the series n=1 3n+1 ln(n+1) is convergent or divergent.

A: : since,1< ln(n+1),for n>2 so, 0<(n^2)/(((3^(n+1))*ln(n+1))<n^2/n^4=1/n^2,  since…

Q: 3t 2t - 1 1-t 1+t [][] 3 and B(t) = 51² 51³ t Verify the product law for differentiation, (AB)' =…

A: See the details solution in below

Q: If lim f(x) = ·∞ then which of the following is true?

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Q: When is a function Fan antiderivative function f? of a if F(x) is continuous for all x in the domain…

A: We know that,  if a function F( x) is called an antiderivative of a function of f( x) if      F'(x)…

Q: _z = g(x,y)=√x² +2y²

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Q: 22 Given the cross product of 2 vectors u and vis, u x v= -3i-3j+3k, and their dot product is,…

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Q: The graph of f is given below. -2.5 -2 -1,5 Why is f not differentiable at x = 1? Of is continuous…

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Q: 3. A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A…

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Q: 41- - ST x² coscyldy dz dx

A: ∫ cos(y) dy= sin(y)+C

Q: 4. Determine if the following lines intersect. If the lines do intersect, state the solution. If the…

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Q: Find the general solution of the given differential equation. xdy-y=x² sin x yw Give the largest…

A: Explanation of the answer is as follows

Q: 29. Given dx where a>0, at what value of p will the integral become convergent? c. p = 1 a. p> 1 b.…

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Q: What is the derivative of y = √/x? 1x² X 2 2 1 X X 2 23

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Q: When is a function Fan antiderivative function f? of a if F(x) is continuous for all x in the domain…

A: Given , When function  F(x) is called an antiderivative of a function of f(x).

Q: What is f 5√xdx? 3 f 5√√xdx = 5x² + C 2 3 f5√xdx = 10x² + C 3 f5√xdx = 5x² + C 3 [ 5vxdx= 5x? +C

A: Let's solve given integral.

Q: 17 For what value of k will the following system of equations have an infinite number of solutions?…

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Q: [x-y tan¹¹(y/x)]dx + x tan ¹(y/x) dy = 0 ydx = (x + √/y² = x²}} 2 2 - dy

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Q: Given w= y² arctan(xyz) + 2x ln(xz). Determine მყ მთ = y + 2y arctan(xyz) + 2x ln(xz) = y[2…

A: We can solve this as follows:

Q: 12-1 40-8 Let A = -4 and b = b₂ Show that the equation Ax=b does not have a solution for all…

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Q: Given the graph below, what can you say about the function at x = -2? Not Continuous Continuous

A: A function f(x) is continuous at x=a if and only if limx→a f(x) = f(a).

Q: - S™ SX x² cos cyldy dzdx

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

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Q: y²-6x²y=-9x ; y' at (1,3)

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Q: Find the exponential function f(x) = Cbx whose graph passes through the points (1, 6) and (3, 24).

A: To find the exponential function satisfying the given conditions.

Q: The graph of f is given below. -2.5 -2 -1.5 Why is f not differentiable at x = 0? Of is continuous…

A: Given graph of a function f.

Q: Given the graph below, what can you say about the function at x = -1? Continuous Not Continuous

A: Explanation of the answer is as follows

Q: 3. | rV3 – adr -

A: We have to find out solutions

Q: Determine whether the series Σn=1 3n+¹ ln(n+1) is convergent or divergent.

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Q: 2. Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1. 2

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Q: Find y'. tan(x + y) = x + y

A: Solution ) tan ( x + y ) = (x + y ) Differentiate with respect to x d/dx tan ( x + y ) = d/dx ( x +…

Q: Evaluate the derivatives of the following functions using implicit differentiation. Write your…

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