Let g(8) = (2s – 1)°. Then g'(8) is 9'(1) is 9'"(8) is and g''(1) is

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: Expand the binomial using the binomial theorem. Show all of your work. (z- 4) °

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Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A: Given query is to find the value of the integral.

Q: partial fractions to frd use 2 |- x9 + x8 2 3

A: Using partial fraction solving the given integration.

Q: Evaluate the definite integral. + ej+ dt - 1) i - (e" - 1) j +k O e? i+ (e-1-1) j+국k 2.

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Q: 3n 8 If tan 0= find the exact value of each of the following. 2 cos (20)

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Q: Determine whether the sequence converges or diverges, and, if it converges, find lim an: n-00 3 - 1n…

A: We have to find the limit

Q: 3n° + 2n³ - 7 {a,}== 7n' + 3п +4

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

A: Ratio Test : Suppose we have a series  ∑ an.Define,   L =limn→∞ an+1an .The,(i)  If L<1 then…

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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Q: Determine the area of the gtven reglon. y = x + sin X Step 1 Note that for the glven reglon, x…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: pind tue indefinete integral S In(s-1) ds

A: ∫ slns-1dsLet u=s-1=∫u+1lnudu=lnuu22+u-∫12u+2du=lnuu22+u-u24+uSubstitute back…

Q: Use the definition of Taylor series to find the first three nonzero terms of the Taylor series…

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Q: F(x) = e2x C = 0

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Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: Consider the system of differential equation x' = 5x – 3y - y' = 9x + 9y Write the system in matrix…

A: To find the matrix A.

Q: The Mean Value Theorem states: For any function, f, differentiable on (a, b) and continuous on [a,…

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Q: Find the coordinates at times t = 0, 5, 10 of a particle following the path a = 9+ 5t, y = 2 – 7t3.…

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Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 00).…

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Q: 8. Find the limit: lim E1(1 130 noisieoq Isisinle bna baoes 1aq d00

A: The detailed solution is given below Thank you

Q: o) rind all veluees of x for which fue Canveryes. for there helues of x, wnite tul fum of tue senes…

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Q: d²y Q2: find of the following statement dx2 a) y = xcosnx b) y = In x3 + ex + cot x

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Q: The junior class has 50 students. Fifteen students take only French, 5 students take only Latin, and…

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Q: The probability that an event will happen is . What is the probability that the event will not…

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) (1 + x)3 Σ 00 f(x) n =…

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Q: The letters r and 0 represent polar coordinates. Write the given equation using r-4 cos 0 Complete…

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Q: Answer the following True or False: Let f(x) be a differentiable function, such that f(– 1) = - 5…

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Q: Write the equations in cylindrical coordinates. (a) 3x² – 6x + 3y2 + z² = 5 z = 7x2 – 7y2

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Q: y =x und y = x+2 ... evolve the area about the line x 3. Using cylindrical shell method, the volume…

A: The cylindrical shell method gives the ,Volume on revolution about a line is given by…

Q: 3. (D² + 1)y = sec² x tan x. %3D

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Q: Find the direction angle of v for the following Vel v = - 6i- 3j What is the direction angle of v?

A: On solving this we will get

Q: Find the gradient vector field Vf of f. f(x, y, z) = xSye'/z Vf(x, у, 2) %3D

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Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

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Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find «(t). r(t) = 8 cos(7t)i+ 8 sin(7t)j + 3tk…

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Q: -2

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Q: Determine the convergence or divergence of the series using any appropriate test from this chapter.…

A: This question can be solved using the concept of geometric series test and p series test for…

Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

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Q: State where the power series is centered. (-1)"(2n – 1) „n Σ * 2"n! n = 1

A: Solving

Q: 1 Σ 6" - 5 n = 1 8

A: Given :

Q: (D² +1)y = sec x. %3D

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Q: Solve the equation cos? x - cos x = 0 over the interval [0°, 360° ]. solving for cosx, solving for…

A: We will solve for cos x and x.

Q: long

A: We will use long division method.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your cnswer to two decimal piaces when…

A: Solving

Q: 0 in quadrant II, find the exact value of: 81 If sin 0= sin 0+ sin 0+ 6. (Type an exact answer using…

A: topic - trigonometric identities sin(a+b)=sin(a)cos(b)-cos(a)sin(b)

Q: Find the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: Differentiate the following using implicit differentiation 3/a + V = 7

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Q: 3/2 x*(G²- x²) %z

A: …

Q: 5. f(x) = (3x² + x)e5x² %3D

A: Explanation of the answer is as follows

Q: Problem 4. The third term of a geometric sequence is 9, and the common ratio is 2 Find the fifth…

A: Given :3rd tern of GP is 9common ratio=32

Q: 4) Find all values in the interval [-27,27]at which the graph of f has a horizontal tangent line.…

A: topic- functions and derivatives