The power series representation of 8. f (x) = x +7 centered at x = 2 is: 8 8 8 8 (x-2) + 81 (x-2) 2- 729 (x-2) 3+.. 6561 - - 7 7 (x-2) + 100 (x-2)2- 1000 7 (x-2) 34 10 10000 O 17 8 (x-2) + - 81 8 (x-2)2- 729 8 (x-2) 3+... 6561 9. 1 8 (x -2) 81 8 (x-2)2+ 729 8 (x-2) 3+.. 6561 9. none

Q: Let R be the finite region enclosed by the curve y = 6x(3 – 2x) and the x-axis. Let V be the volume…

A: See the solution in below

Q: sin(x²) Evaluate lim 140- e2r – 2x – 1

A: Topic = Limits

Q: Enclosing an Area Patricia wishes to have a rectangular garden in her backyard. She has 64 ft of…

A:

Q: 4. (D2 – 5D + 6)y = 15sinx – 15cosx -

A:

Q: Solve the differential equation dy + y = 4xy³, y(0) = dx %3D 1.

A:

Q: a spherical balloon is filled with gas at a rate of 300 mm3/sec. Find the rate at which the surface…

A:

Q: On what interval(s) is f'(x) increasing? Decreasing? Explain.

A:

Q: Find f'(4.8)

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

Q: V. ASSESSMENT (Time Frame: (Learning Activity Sheets for Enrichment, Remediation, or Assessment to…

A: Given

Q: 2л + 3 dx 4г2 — 4х + 5

A:

Q: 5. e(2x- y) = 2x - y

A:

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: As we know the surface area of the cube is; S=6a2                            ...(1) Where 'a' is the…

Q: 12 · x2 – 28 · x + 20 A B Let f(x) The partial fraction decomposition of f(x) where A, B, C E Z. (x…

A:

Q: In a race, Molly starts running from rest at a constant acceleration of 3 m/s. She is running in a…

A:

Q: Given the vector i = (2,0, 1). (a) Solve for the value of a so that u and o= (a, 2, a) form a 60°…

A: Given the vector u→=2, 0, 1.a To solve for the value of 'a' so that u→ and v→=a, 2, a form a 60°…

Q: -2 Sx'V4 – x²dx

A:

Q: dx 4е2я — 8ет + 5

A: This question can be solved using the concept of special integrals.

Q: Evaluate the integral. (2 4y2 – 7y – 12 J. yớ + 2)y – 3)*

A:

Q: Which of the following is true for the graph of Ax) on the interval (0, 2)? (Circle ALL that are…

A: The graph of the function fx

Q: Let C(x)= x2+4x+1 dollars be the cost function, where the x represents the quantity. The estimate…

A:

Q: (80") (7")(9") + 1* n=1 IM:

A:

Q: = )* - a) Va' + 1) zVx +1 +C b) Va' + 1) - 2V +1 + C Q3: S dx%3D c) V + 1

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

Q: f(a + h) – f(a) =

A:

Q: The salution af the hamegenous eauabion (X+gcat

A:

Q: b. dx Vr - 2x2 + 1

A: To evaluate: I=∫x5x4-2x2+13dx=12∫x22(x2)2-2x2+132xdx Substitute x2=u⇒2xdx=du

Q: The solution set of non-negativity constraints is located at Y-axis Quadrant II 3- QuadrantI X-axis…

A:

Q: Differentiate each function by applying chain rule. Match each item to a choice: y = x(x² + 3)² y =…

A: We have to differentiate following functions using chain rule: y= x(x2+3) 2 y= (4x-10) 4 y=…

Q: Consider f(x) = cos (x) ln(x +2). a. Find the local linear approximation of f(x) at xo = 0. (In 2 z…

A:

Q: Let R be the finite region enclosed by the curve y = 6x(3 – 2x) and the x-axis. Let V be the volume…

A:

Q: Assume that the radius r of a sphere is expanding at a rate of 10 cm/min. The volume of a sphere is…

A:

Q: 3) (0,1,0), (2,1,0), (3,4,7) Ans. Indepena

A: Given

Q: Find the following antiderivatives. Cosh sinh r - 1 cosh r dr (a)

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Let f(x) - 16. The arc length of the graph of f(x) over the interval [5, 9] is given by the definite…

A:

Q: derivative(y

A:

Q: Let f(x) = ax* + bx² + 50. Determine the values of a and b so that f(x) has a point of inflection at…

A: We have to find value of a and b

Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: Here, given that: yc=c1x2+c2x3⇒y1=x2, y2=x3 And, u1=2x-3x2, u2=2x+3

Q: .C find the firet order parhal dervohve f 4.5 1. z) = e 32 W="y - 10y2³ + 432 hCs, t) =° t?In ts) +…

A:

Q: Use the substitution u = 4x2 +1 to convert the integral fo ret+1 dx to an integral of the form Sº…

A:

Q: Find the general solution for the given differential equation. dy dx

A: To find the general solution of the given differential equation.

Q: dx (x-2) Jx12

A:

Q: Find a formula for the nth term of the sequence. - 1, 4, - 9, 16, - 25, ... Determine the sequence's…

A: Given sequence is -1             4                 -9                16              -25 By…

Q: The series 1 + vn- 1 + Vna n=1 8

A:

Q: Question 7 The outer diameter of a spherical tank measures 6 feet. If the tank is made with a…

A: This question is related to volume of spheres, we will solve it using given information.

Q: II. Find the Inverse Laplace of the following 2s-9 d. s² +2 1 е. (s²+1)(s²+4s+8)

A: As we know the Laplace transform identity; 1). L-11s2+a2=1asinat 2). L-1ss2+a2=cosat 3).…

Q: V9 – x² .2 .2

A:

Q: What are the local extreme values of the function f(x) = x³ – 3x + 2?

A:

Q: dx J Tx2 – 25

A:

Q: dy By using implicit differentiation, find dx for xy + e* = sin(x+1). (x.y)-(1,0)

A:

Q: In Exercises, the given vectors form a basis for a subspace W of R' or R'. Apply the Gram-Schmidt…

A: The given vectors of ℝ3 are: x1=110, x2=342

Q: Find the linearization L(x,y) of the function at each point. f(x.y) = x² + y? + 1 а. (2,1) b. (0,2)…

A: