1a: Find the values of a and b, if any, that make f(x) continuous everywhere. If no such values of a and b exist, explain why. Note: express your solution based on the question asked in a well-organized, clear and concise way. f(x) = x² 4 x-2 ax²-bx+3 2x - a+b for x < 2 for 2 < x <3 for x ≥ 3

Q: 4. A = -1 0 5-2 245 0 -3 , B= 7 650 -3 -4 2 -1,c=7,d=5 7 9

A: we are given the matrices and we need to find out the matrix cA+dB

Q: Compute the limit of a sequence. a. Find the limit of the sequence a n n+70 2 √n² Vn +7

A: Since you have asked multiple questions in a single request, we would answer only the first question…

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A: Find the exact length of the curve.36y2=(x2−4)3,2≤x≤6,y≥0

Q: 2. Determine d (sin-¹(x²-1)). dx Simplify your answer as much as possible.

A: Consider the function

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Q: Answer the following questions for the function f(x)=x√x² + 16 defined on the interval -6 ≤ x ≤ 6.…

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Q: Simplify the rational expression. y³ - 27 -y² + 9y - 18

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Q: f(x)=x54x

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A: The given function is

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A: Given (x-4)(x+4)

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A: =3

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A: Given, .Given, s(4)=12.

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Q: purchases a new car for $21,550. He makes a $6000 down payment and finances the remainder thro tized…

A: We have to find the monthly payment, amount and interest.

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Q: Given F(1) = 1, F'(1) = 1, F(2) = 3, F'(2) = 7 and G(2) = 1, G′(2) = 5, G(3) = 6, G′(3) = 2, find…

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Q: 7x 1+2x 2+1 x_3+8 x_4+9x_5 = 69 9x 2+3 x 3+4x_4+4 x 5 = 54 4x 1 + 6 x 2+5 x_4+4 x 5 = 40 2x 1 + 10 x…

A: We solve the following system of linear equations using the Gauss-Jordan Elimination Method:

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Q: Use the chain rule to find the derivative of 6√3x5 + 9x8 Type your answer without fractional or…

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Q: The velocity of a particle moving along a line is a function of time given by 79 t² + 12t + 27 v(t)…

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Q: Evaluate the integral by reversing the order of integration. 1 1₁² X 4 y³ + 1 dy dx

A: given

Q: Determine the derivative with respect to a: In (255)

A: Given, .We know,

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Q: Multiply: (2+5i)(2−13i). Give your answer in complex standard form a+bi.

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Q: Differentiate. f(x)= x³ In 7x 3 f'(x) =

A: Product Formula for differentiation is given as follows

Q: 1. Let g(x) = ln ((f(x))² + x). Determine g'(5) if f(5) = 2 and f'(5) = 3.

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Q: Find the eigenvalue associated with the eigenvector A = Number -[-28] = of the matrix A=

A: The given eigenvector is The given matrix is

Q: (a) Let f(x) = arcsin(x). Compute the following quantities. f(1/2) = Number f'(1/2) = Number (b) Let…

A: (a) f(x)=arcsin⁡(x)

Q: If f(x) = 4√√x(x³ - 8√√x+6), Find f'(2). find f'(x).

A: If .To find .

Q: Verify that fxy = fyx for the following function. f(x, y) = 3x5y6-9x4y³ fx =

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Q: 2. A = 77₁b = 3 25 -1 3

A: Given, .If A=, than .

Q: Match the third order linear equations with their fundamental solution sets. 1. y" - 9y" + 20y = 0…

A: Match third order differential equations

Q: (Multiple Choice Question) If sec a = -3 = tan ß and a, ß € [T, 2π], then sin(a + 3) is equal to:…

A: Given that and

Q: 5. Solve the second-order equation xy" +2y' = 12x² by making the substitution u=y'..

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A: we are given the differential equation and we need to find out the solution.

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A: The curve of the function f(x) is shown as,

Q: A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the…

A: Given that a model used for the yield Y of an agricultural crop as a function of the nitrogen level…

Q: Find the present value of $2000 payable at the end of 3 years, if money may be invested at 4% with…

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Q: question 3

A: Figure

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A: Given, x =9-t2y = t3-12t

Q: d) If k(x)=3 find the values of a and b such that k(x) is differentiable at x = 3.

A: Note:-Since Q 4 is  incomplete but part d is complete then we solve part d for you.The given…

Q: -4 -3 -2 -1 4 3 2 1 -1 -2 -3 -4 1 2 3 4 20x For the above rational function f( x ) = 3.5r2 +3…

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Q: Please complete parts (d) and (e)

A: To solve part d and part e, answer of part c is required.