Answer: dy = 3yCx'ty)

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A: Answer : y=5sin(x/3)

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Q: Determine whether the following series is convergent divergent. or (-1)"3n² 4n2–1 n=1

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Q: I. Evaluate the following integrals. 1 d.x J #(9 – In² x)5/2* 1. -

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Q: x² +64 Using trigonometric substitution, given dx, the simplified form of the integral is: x2 […

A: Use trigonometric substitution,

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Q: Solve for the general solution of the following differential equation and determine whether it is…

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

Q: Find and dx d²y then simplify whenever possible. dx2 1) y = 3t5 – 2t , x= 4t³ |

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: xsin(x³) dxdy

A:

Q: Consider the parallelepiped with adjacent edges u = 3i + 3j + k v = i+j+ 8k w = i+ 9j + 5k V Find…

A: Given;  u=3i+3j+k v=i+j+8k w=i+9j+5k.

Q: хах can be solved by either algebraic subsitution or integrataion by parts. x-1 (A) True B) False

A: To determine whether the given statement is True or False.∫x dxx-1 can be solved by either algebraic…

Q: sin x Let g(x) = . 1 Find the derivative a'(x). dt . 2 1+t3 cos? x 1+ sin x sin x 1+ cos³x cos X 1+…

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Q: Compute the value of the improper integral. (If the integral diverges to oo, type o0; if the…

A:

Q: Use tabular method to evaluate ƒ –2x³e¬5×dx

A: Solution is given below:

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A: i have provided this answer with full description in step-2.

Q: Determine whether the following series converges or diverges. If the series converges, determine the…

A: 1)∑n=1∞ cos2πnan=cos2πnApplying series divergence test;limn→∞ cos2πnlimn→∞ cos2π∞=cos2(0)=1limn→∞=1…

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A: Given

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A: Convergent

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Q: = > Σ 5. For all x E R, e* п! Express f (x) = x²e* as a power series. b. Find the third-degree…

A: We have to solve questions based on Series .

Q: To input your angle measures in degrees, use the functions sind (5), cosd (5) and tand (5), instead…

A: This is a problem of a trigonometry. Based on application of trigonometry. Please follow the below…

Q: S 3x5V1 – 2x³dx

A: Use simple integration formula.

Q: Is the function continuous on the interval (0, T COS x O no O yes O cannot be determined

A: Given problem:- Is the function ex/cosx continuous on the interval [0, π] ?

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Q: I 3n O The region bounded by y = sin x and x- axis on the interval [-

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Q: JVVy+1-2 dy can be evaluated conveniently if we let x =VVy+1 - 2 and dy = 4x(x² +2)dx. (A True B)…

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Q: 2-x Q1) Evaluate the integral S* dy dx using polar coordinate

A: Given,According to question,Given integral,Let I = ∫01∫x2-x dy dx

Q: etermine if the given converges or diverges. Find the value if it converge. | In(x²) dx -1

A: To integrate the given function.

Q: [ 3x3-2х2-4х-3 х2 (х2+x+1)

A:

Q: The plane N contain the points P(1,–4, –5) and Q(2, 1, –3). Moreover, it contains the line 1 3 -x =…

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Q: 4 ds = 1 2.

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Q: xy + y² dx dy Find the general solution of x2 dy Solve 2xy dx x² + y? given that y = 0 at x = 1

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Q: do 3 (6eº + 1)3

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Q: 1 dt. o t4 +5 Let f(x) = Find the derivative f'(x). none of the choices ex e2x

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Q: Using homogenous differential equation determine the particular solution of

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Q: 4. (a) Find the vertical and horizontal asymptotes. (b) Find the intervals of increase or decrease.…

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Q: 1 2n 1. Consider an = tan-1n a. Determine if the sequence {an}n=1 converges or diverges. b. Is the…

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Q: Determine the derivative of each function using the limit definition. 1. Y = 2 – 7x - 2 = 4 – 5x –…

A: f'(x) = limh→0 f(x+h)-f(x)h.

Q: A. LIMITS Limr - 25 1.) lim VE – 2 2.):-4t-4 x-5 x-5

A: Here we have to find the limits.

Q: 0/ using the test comparing the series Enas n?_2n-3

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Q: 1 dx (e2r – 4)5/2

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Q: Find Duf at P. 1 1 f (x, y) = 5(4+ xy)3/2; P(3,4); i+ j и %3 V2 NOTE: Enter the exact answer. Duf =

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Q: Find f(100)(x) if f(r) = (x + 2)100. a. 0 c. 100! = 100 x 99 x 98 x 97 x ... x 2 x 1 b. 100 d.…

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Q: Find the derivatives of the given functions. a. y = [ Arc sec(tan x)|· e »<2x

A: use logarithmic function to evaluate the derivative.

Q: y = (cos COS T 4x5

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Q: 3 5). | e2x dx -1

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Q: 8. [sin? x cos' x dx Ssin*

A: (8). Given: I=∫sin2xcos5xdx   As we know from the trigonometric identity; sin2x+cos2x=1 And The…

Q: Find Duf at P. f (x, y) = 3(4 +xy)2; P(4,3); u = 1 i+ j NOTE: Enter the exact answer. Duf

A:

Q: I. Evaluate the following integrals. 1 1. -d.x x(9 – In² æ)5/2°

A: Given