Find an implicit and an explicit solution of the given initial-value problem. dy y – 1 dx x? - 1' y(2) = 2

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A: To evaluate: I=∫e2x4e2x-8ex+5dx=∫(ex)24(ex)2-8ex+4+1dx=∫ex4((ex)2-2ex+1)+1dx=∫ex4(ex-1)2+1dx

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A: integration

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A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Given problem:- r₁:  A = (3,2,4) m=i+j+k r2 : (2,3,1) B = (4,4,1)   (a) Create Vector and Parametric…

Q: e2" (18 + 5t – 2) 6 + 5(s – 2)² – 2(s – 2)³ (8 – 2)ª 2 - (8 – 2)* (s – 2)² Option 2 Option 3 6 (s +…

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Q: Find a formula for the nth term of the sequence. 1, - 16, 81, - 256, 625, ... Determine the…

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Q: 4 a. Use implicit differentiation to find the derivative dy/dx of the given function. b. Find the…

A: The objective is to find the derivative and slope at the point .

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Q: (2) Evaluate the iterated integral by converting to polar coordinates. 2 v8-yz Vx2 + y² dx dy o y

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Q: 14 y=7x-x 12 10 8 6 (6, 6) 4 y = x 2 4 6. 8. 2.

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Q: S 23x* + 5 +* x2-16 dx X-4

A: We will use simple Integration rules to solve this question.

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A: answer is in next step

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Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

A: A detailed solution is given below.

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A: Let's find.

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Q: Find and classify all critical points of the function defined by h(x,y)=x^3−3x+3xy^2.

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Q: Consider the points A(2, –1,3), B(7,0,5) and C(0, 1, 7), and the line l with symmetric equation 3 =y…

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Q: 10. A boy is flying a kite on a string. The kite is 120 ft above the ground and the wind is blowing…

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Q: Find the Laplace Transform of the functions PLS ANSWER ASAP

A: We need to find laplace transform.

Q: Determine the sum of this convergent series.

A: This question can be solved using the concept of infinite geometric progression.

Q: A force of 20 Ib is required to hold a spring stretched 8 in. beyond its natural length. How much…

A: solution:-force, F=20 lbspring stretched,x=8 in=812 ftfor springF=k·x20 lb=k812 ftk=20 lb812 ft=30…

Q: DEFINITION

A: We will find the Laplaces Transform.

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Q: Find dy/dx if ylnx + y^2 = 0.

A: According to our guidelines, we can answer only one question or three subparts of a question.

Q: -2t e "(cost+3 sin t)

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Q: Evaluate the indefinite integral. for, sin( + C

A: Product Rule of integration : ∫u.v dx= u∫v dx - ∫dudx∫v dxdx .

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A: Given :2eln cos2t

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Q: 4) lim (5x-1 + 1)4x x00

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Q: Use the Root Test to determine whether the series convergent or divergent. n2 + 1 9n2 + 8 n- 1…

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