Solve using the U-Technique Question 10 For ſk*e3*dx = 1 (ke)3x 3 (1–In 2-1) If u = 3x, then k =? ... 1 A 8 1 B 2 2

Q: Solve using the U-Technique Question 5 The integral / 2 *)cos(2*) dx takes the form k/ cosu du when ...

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Q: If S(16x4 – 16x³ + 4x²)dx = F(x) + C, then F(x) ?

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Q: Use sigma notation to write the Taylor series about x = xo for the function. 6 In r; xo = 1

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Q: What is the value of 7/2 r(3 cos(x) + sin(x))dr? 7/2 Give your answer as an integer or as a decimal ...

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Q: 1. Evaluate (3260)"]" × (-5+ j6) (cos(3 + j5)]1-/) Sin sin-

A: We have to find: sin-13∠60°3*×-5+j61jcos3+j51-j. We will find the interior parts first on different ...

Q: Find the indefinite integral. J. x cos 107Tx2 dx

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Q: 5. The standard form of the first order linear differential equation dy-(cscx-ycot.x)dx=Ois %3D

A: As we know that; The standard form of the first order linear differential equation; dydx+Py=Q Where;...

Q: Determine whether the alternating series converges. k + 1 E(- 1)*+1. 3k + 1 k=1 O The series diverge...

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Q: Write the factored form of the

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Q: Determine f(x) so that cos(In²x) f (x) dx = sin(In²x) + C

A: Let t =log2 x and follow step 2nd . 

Q: I. Identify the elements for the following set expressions given the sets below: (Explain your answe...

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Q: Evaluate the limit. If dne, explain. (2cos(4x² + 7) + [6x² + 4] lim X→+∞ 4x2 + 7

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Q: Find the derivative of y with respect to x for y = sinh 1(11/15x). dy 165 dx 2/1815x? + 15x

A: Given query is to find the derivative of the expression.

Q: Find the particular antiderivative that satisfies the following conditions: 10 10 H' (x) x2 ; Н(1) —...

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Q: Evaluate the integral by making a u-substitution and then integrating by parts. NOTE: Enter the exac...

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Q: Use the difference a+1 – an to show that the given sequence {a, } strictly increasing or strictly de...

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Q: Suppose an object in circular orbit stops in a position where cos(0) The terminal point is 13 locate...

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Q: Write the first five terms of the sequence: 11 ln n) +oo Determine whether the sequence converges, a...

A: To write the first five terms of the sequence.11 ln nnn=1+∞To determine whether the sequence converg...

Q: Write the first five terms of the sequence, give the exact answer: +00 In +1Sm-1 Determine whether t...

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Q: Eliminate the parameter to find a Cartesian equation of the curve, for – x(t) = 100 tan² t y(t) = – ...

A: We are a parametric equation of curve as follow: x(t) =100 tan2t  y(t) = - 12sect Where -π/2 < t ...

Q: 4. Given: a, = 5, a4 = 13 Find: d =? а. 1 b. 2 с. 3 d. 4

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Q: Given that the graph of f(x) passes through the point (5, 2) and that the slope of its tangent line ...

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Q: Suppose that f(z) is an entire function and there exists aceR s.t. Re(f(2)) < c for all z. Show that...

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Q: Given: (25(x)dx e-x3 There is a function f (x) such that when u = -x³, the resulting integral is f 2...

A: Let's find. 

Q: The owner of a cattle ranch would like to fence in a rectangular area of 3000000 m² and then divide ...

A: Solution is written in below steps.

Q: k If u = f (x), then f dx x4+2x2+1 +C for some constant k . Compute kf (1). x2+1 %3D

A: We have to find kf(1).

Q: dx The integral S reduces to S k, where u = f(x) and for some constant k . Compute f(1). ex+1

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Q: . 2:(y-x² }tx+dy=0

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Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: At noon, ship A is 140 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing no...

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Q: What is the slope of the TANGENT LINE to the given curve 1 y = x + at point where x.= -2

A: Slope of tangent is    m=dydxdydx=1-1x2

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. Σ (-1)*+1 k7/6...

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Q: 1. Given: a2 = 12, a3 = 24 Find: ao =? a. 2 b. 4 с. 3 d.

A: Topic:- sequence and series

Q: 1+ In x Find f(x) so that when u f(x) the integral tan( fx) dx can be rewritten as cot u du. A) x- x...

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

A: The given series is: ∑k=0∞56k+3=563+564+565+566+... which is a geometric series with the first term ...

Q: Let A= [a, b c, d, e) and B=(a, b, c, d, e f g, h). Match the given sets in the left to the sets in ...

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Q: 1. 4(х- 3) 2. 2x( 2x + 2) 3. Зx(x-4) 4. 4x(x +7) whn

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Q: Given: ((x)dx Evaluate f(v2). There is a function f(x) such that when u = -x³, the resulting integra...

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Q: Set up a definite integral with respect to x (dx) (set up only, do not evaluate the integral) to fin...

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Q: . The standard form of the first order linear differential equation x y'+xy +2 = 0 is,

A: This question is based on to form a standard first order differential equation.

Q: Determine whether the series converges. k=1 The series

A: Ratio Test : Suppose ∑ak be an positive term series and                         limk→∞ ak+1ak =L , t...

Q: Make a 1 rational equation problem involving 3 rational expressions with binomial term with solution...

A: We have to form a rational equation problem such that it contains 3 rational expressions and each ex...

Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos 4x-...

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: Use sigma notation to write the Taylor series about x = xo for the function. 4 In x; xo = 1

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…=0+ddx...

Q: Question 13 Using u-substitution, the integral S f(x)dx reduces to a new integral ſ g(u)du. If g(u) ...

A: Here, given that: ∫f(x) dx=x+ln (x-1)+c...(1)

Q: y = Vx – 7 ,(7,0) -

A: Solution is written in below steps.

Q: 2:(y-x² )dx+ dy =0 1.

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Q: Let J ex+1 S dx be given . If u = e* + 1, then the resulting integral is S f(u) du. Compute f(3).

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Q: #1 only

A: Topic:- differential equations

Q: Find the particular antiderivative that satisfies the following conditions: 10 10 H' (x) Н(1) %— 0. ...

A: H'(x) = 10/x2 -  10/x7 find H(x) = ? so we have to integrate it H'(x) = 10x-2 - 10x-7 H(x) = -10/x +...