Solve the IVP using Taylor's series( 3rd deg polynomial). dy/dx= 3x2y; y(1)=1 y'(1) = y" (1)= y" (1)= y(1.4)= True value at x=1.4 (2 decimal places) (2 decimal places)

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

Q: n(3x)+sin(5x - 4) - 3 Using Centered Differencing. h = 0.002 O 4.86693212 O 4.876145534 D…

A: Equation is f(x) = ln(3x) + sin(5x - 4) - 3

Q: Pr[A'nB]=0.4 and Pr[(AUB)']=0.5. determine Pr[A]

A: GivenP(A'∩B)=0.4P(A∪B)'=0.5

Q: y aln(a) – y = 0; y(2) = In(4)

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Q: If y = (4x + 7), find y' (1). O 11 ln(11) + 4 O 11 ln(11) O - O 11 ln(11) - 4 In(11) – - In(11) + 4…

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Q: 3) Estimate Y(2) using Euler's method with 0.5 long dY intervals. Y - 2X and Y(1) = 0. dx

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Q: .E(y) = -1.5 E(x) = 15. y = (0.1)x – 3 correct Error

A: Given that, E(y)= -1.5 And E(x)= 15

Q: 14. Find k'(s) if k(s) Ins %3D s2 а. 2s2 b. s4 2 In s C. s3 s3 2 Ins 1 d. s3 s3

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Q: 5. Evaluate tan (x)sec'(x)dx

A: Find the integral by using substitution

Q: What is the approximate value of the first derivative of S(x)=-01x-0.15x-0. 5x-0.25x +1. 2 at x-0.75…

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Q: thod for the fünction using the given initial guess. (Round you x2 - 5, x1 = 2 f(x.) f(x

A: Given, Using Newton's Method Iteration fx=x2-5,x1=2

Q: (x+2) (2x+1)° * (3x+1) [2] Consider y= where x > 0 dy First take Natural Log of both sides then find…

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Q: 4. [csch(x)] = -csch(x) coth (x) dx

A: we know thatdifferentiation of cosh(x) is sinh(x) and vice- versa

Q: LET F(X) =2 x SIN(X), AND EPSILON = 3 × 10-7. FIND OPTIMUM STEP VALUE THAT CAN BE USED WITH…

A: We are given f(x)=2 sin(x) and ε=3×10-7. The formula for central difference is…

Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: e" dx Find (ez +3)(e –5) Find S In(x)x²dx.

A: The first question can be solved using the concept of partial fraction and the second question can…

Q: Use Newton's Method to estimate one of the zeros of f(x) = e 6 or less iterations. (Note: The…

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Q: If P(A or B) = 0.801, P(B') = 0.33 and P(A and B) = 0.20. Find i) P(B) ii) P(A)

A: Answer: Given that, P(A or B) = 0.801 P(B') = 0.33 P(A and B) = 0.20

Q: в) (2.001)5 (b) у9999

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Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

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Q: Suppose that P(A)=0, P(C|A) =0.006, and P(C'|A')=0.0055 Find P(A∣C).

A: GivenP(A)=0P(C|A)=0.006P(C'|A')=0.0055

Q: Investigate the root of the equation x+Ln x-5 = 0 in the range [3.2,4] using the Regula-Falsi…

A: Consider the given equation whose root is required to calculate.

Q: Suppose P(t) represents the population of a certain mosquito colony, wheret is measured in days. The…

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