5. (4D³ — 4D² + D-1)y=0

Q: 2.] xydx + (x² + y² + y )dy = 0 y(0) = 1

A: To solve the following initial value problem. xy dx+x2+y2+y dy=0, y0=1

Q: 1. Show that the following ODE is of homogeneous degree. Hence solve it subject to the given…

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Q: Evaluate the integral. (Use C for the constant of integration.) x² 3 + 4x 3/2 dx 4x2) 3/2

A: We have to solve given integral.

Q: |x|-5 lim x−-5x2–25 ||

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Q: Let L be the infimum and let U be the supremum of the set {x≤R : 2x² - 9x − 31 < 0} Find the sum…

A: Given set { x∈ℝ  :  2x2-9x-31&lt;0

Q: Find a formula an for the n-th term of the following sequence. Assume the series begins at n = 1. 1…

A: The given sequences, i) 11, -14, 19, .... ii) 47, 58, 69,..... We have to find the formula for nth…

Q: Question #2 - Find the relative extrema for the function f(x)=x²-3x² using the first derivative…

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Q: A person standing on a bridge over a river throws a stone such that the height H (in feet) above the…

A: We can find out the solution by following method.

Q: 3. Determine an integrating factor, dependent only on y, that makes the following ODE exact. Hence…

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Q: Which of the following is a correct classification of the differential equation xy" + 2(y¹)* - y = 0…

A: To classify the given differential equation

Q: 4. Prove that d - (csc (x)) = -csc (x) cot (x). dx

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: aw dr Find when r = 10 and s= - 10 if w= (x+y+z)²₁ x=r-s, y = cos (r+s), z = sin (r + s).

A: see below the answer and calculation

Q: Find the values of x for which the infinite geometric series 1+(4x-3)+(4x−3)² +... is convergent.

A: The given geometric series 1+4x-3+4x-32+...... We have to find the values of x for which the…

Q: 2. Find the derivative of each function: cos (x) 1-x² (b) g(x) = 5√x - √ (c) f(x) = (3x² + x −…

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Q: 4) Find limit Show all work Hint: divide numerator and denominator by x x² + x lim x→∞ 3 - x

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Q: If f'(0)=3, then f is necessarily continuous at x = 0. False True

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Q: Find all the critical points of f(x, y) = 5 — 22² +2²³ y and indicate whether they are local maxima,…

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Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. (-5)"…

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Q: Use symbolic notation and fractions where needed. Enter DNE if the series diverges.) 7.(-3)" 11" =2

A: Given query is to find the sum of the series.

Q: Find f '(x) and f "(x). f(x) = x ex f'(x) = f "(x) =

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Q: Find the Maclaurin series for f(x) = What is the Maclaurin series of Σ n=0 16 1+x 16 1+x -? (Type an…

A: The given function is: fx=161+x  To find the Maclaurin series for f(x).

Q: Evaluate the following integral. 1 -0 J% de √3¯°40-□ de= 0

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Q: ч-тахи-лых

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Q: Determine if the vector field F(x, y, z) = (y − z, x − z, x −y) is conservative or not.

A: Given;  F(x,y,z)=(y-z, x-z, x-y).

Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do…

A: (a)  f(x)=x-72x2+x-72

Q: Question #4 - Find the following for the function f(x)=x²³-6x² +9x+1 a) The coordinates for the…

A: Given: fx=x3-6x2+9x+1 To find: Relative extrema, interval in which function increases or decreases,…

Q: Express the integrand as a sum of partial fractions and evaluate the S- x+9 2x³-18x Rewrite the…

A: Topic:- application of integration and partial fraction

Q: Suppose that an object in motion has position function s(t) = t² cos(5t) where t is the number of…

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Q: Which of the following have the same value sin x with lim? X x →0 lim x-0 lim 1 X-- lim x 0 1 sin (x…

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Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: To find the general term of the sequence, starting with n=1. T determine whether the sequence…

Q: Complete the following problems, Please show all your work and make sure you have answered all the…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: Determine the limit of the sequence or state that the sequence diverges. 7+n-2n² 7n² + 1 (Use…

A: We can solve the given problem by using the concept of limits.

Q: f(x) = √2-4 x+4

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Q: Find the equation of the specified line. y(x) = through (1, 9) parallel to x - 9y = 9

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Q: esinx Q2. S dx secx

A: Integrate by substitute method

Q: Consider the function f(x) = 3, a) Evaluate lim f(x) and lim f(x). x<0 0≤x≤1 √x+2, x≥1 c) Is f(x)…

A:

Q: تر ه

A: Graph of the function is given, we have to find the given limits.

Q: I need to graph f(x)= 2x2+8x divided by x2-x-20. To do this i need to find the following Vertical…

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Q: Find the derivative of the function using the definition of derivative. f(x) = 1.5x². -x+ 2.3 f'(x)…

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Q: This question makes an important point: the maximum point of a function may not always be found by…

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Q: Find |A| for  a) x-y+z=0 6x+2y=24 6x-2z=10 b) x-y+z=0 4x+2y=8 2y+3z=7

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Q: Determine the derivative of = x³. f(x) = x³ when 2. f'(x) 3. f'(x) 4. f'(x) = 5. f'(x) 6. f'(x) =…

A: f(x)=x5xlnxn=nlnxd dx(lnx=1xd dx(a.b)=a×dbdx+b×dadx

Q: lim x--2 1 1 2 + - X 2+x

A: We have to slove above question

Q: Calculate the first four terms of the sequence, starting with n = 1. b₁ = 2 1 bn-1 (Give exact…

A: given bn=bn-1+1bn-1given b1=2

Q: Find the area of the surface generated by revolving about the 2 2 2 3 3 3 x-axis the portion of the…

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Q: 4. (a) Write an equation of the tangent line to the graph of g(x) at x = 2 (b) Find the value(s) of…

A: Given g( x ) = x1 + x2

Q: Consider the function f defined by the formula ax2+bx+a if x ≥ 1, f(x) = 28 -+a if x < 1. Determine…

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Q: Find the derivativ A. f(x) = -2(3x5 + 6x².

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Q: 10. Investigate the behavior and sketch the graph of y = 12 - 5x - 2x².

A: The given function y=12-5x-2x2. We have to sketch its graph.

Q: Əw Əv 2 y Find when u = 0, v = 0 if w=x + + ₁ x= x=5u-5v+1, y = 6u + 6v - 6.

A: To find the indicated partial derivative