Question: Using the substitution rule, which of the following gives the value of the definite integral (x + 1)²dx? Select one: O 7 O 5 O 9 O None of them.

Q: Prove that the given equation is a solution to the given DE: 1. %3D Gjезх + Сzе 2х + Сзе*; у" — бу" ...

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Q: u+1 Using u-substitution, the integral S f(x)dx reduces to a new integral f g(u)du. If g(u) evaluate...

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Q: Evaluate the integral. cos(5 x) dx

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Q: Using u-substitution, the integral f(x)dx reduces to a new integral f g(u)du. If g(u) : u+1 evaluate...

A: ∫f(x)dx = x + ln(x-1) +c we have to find f(x) so we have to derivate the ∫f(x)dx so f(x) = 1 + 1/(x-...

Q: 3. Is the function given by Sx-4x-5, メ<5 X-5 2. continccus at x =52 Why ar whynot ?

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

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Q: 3. When the linear differential equation is multiplied by become an an integrating factor the equati...

A: We have to fill on the blanks. 

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. k Σ 2ln k k=2 ...

A: We know about conditionally convergent when series absolutely divergent.

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

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Q: (x – h)? + y? = r² O y " +(y')² + 1 = 0 O y" +(y')² = 0

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Q: Determine the area and circumference of the following circles. 17. 18. 19. 5 in 5 in 28 cm

A: Area and circumference of a circle

Q: If cotx 12 find the other trigonometric functions

A: We will use the basic trigonometric formulae to solve this question.

Q: Question 20 csc x du 3T If u = f(x), then dx = Compute f и sin x – cos x A B 1 D -1

A: We have to solve our question

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t аnd x = sec-1 t

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Q: Find f (x) so that when u = f(x) the integral J tan(f(x) 1+ In x dx can be rewritten as cot u du. %3...

A: ∫1+ln(x)tan(f(x))dxlet u=f(x)=xln(x)⇒u=xln(x)differentiate on both sidesdu=(1+ln(x))dx

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: Solve the differential equation. 5y' = 4 ex/5 + y + y The solution is y = 4x +C X 5 5 e (Type an exp...

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Q: (ke) 3 (1-In 2-) 1. For Sk*e3* dx = +C.f u= 3x, then k=? 2.

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 00 (-1)k+1 k8/...

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Q: Determine the following equation if it is Homogeneous IVP, First, second, higher order equations and...

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Q: If f(16x*- 16x³ + 4x²)dx = F(x) + C, then F(x) %3D

A: Formula:∫ xn  dx  = xn+1n+1 + C   Integral:I=∫ (16x4-16x3+4x2) dxI=∫ 16x4 dx -∫16x3 dx +∫ 4x2 dxI=16...

Q: (2х — Зу + 2)dx - (3x + 4у-5); У-3) %3 4 |

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 5 P4(x)

A: taylor series

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

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Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile i...

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Q: 3. Is the function given by Sx-4x-3, メ<5 X-5 メ+1,xM5 continccus at x=52 why cr whynot?

A: topic - limit and continuity

Q: 3 find the limit if it exists .If it do esn't exist, explain why. lim 13+x| X-> -3 2(34+X)

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Q: if 4x1

A: Given problem:-

Q: Given the following series (-9)" I. E-1(VZ – 1)" II. En-1n10"+1 5n (-1)" En-1 ninn -2n IV. En III.

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Q: 1-2n The sum of the series 1 is: A) 1. B) 2. C) D) E) Diverges.

A: The given series is: ∑n=1∞121-2n which can be rewritten as: ∑n=1∞1212-2n=12∑n=1∞2-1-2n=12∑n=1∞22n=12...

Q: 2. Given: a1 16, а4 1024 Find: az =? а. 12 b. 18 с. 36 d. 64

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Q: 2.ly-x dx+ dy = 0

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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: Write the first five terms of the sequence: {Vn² + 7n – n} +00 Determine whether the sequence conver...

A: Given: ∑n=0∞n2+7n-n

Q: Write the first five terms of the sequence: {13a"} ´ 13 In n ] +00 n n=1 Determine whether the seque...

A: {13ln(n)n}The nth term of the sequence isan=13lnnna1=13ln(1)1=0a2=13ln(2)2a3=13ln(3)3a4=13ln(4)4a5=1...

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 Taylor polynomials of orders n = 0,1,2, 3, and 4 about x = x0 and then find the nth Taylor ...

A: f(x)=13sin(πx), x0=92

Q: 0. Refer to Problem 19: How fast is the circumference of a circular ripple changing when the radius ...

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Q: (х + 2) dx (x + 3) sin y cos y dy In(x + 3) sin? y + C - ans. 2 2.

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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: For the following primitives, identify the number of essential constants.(x and y are the variables)...

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Q: Problem 2. Do both part a. and part b. Find the maximum or minimum value of the quadratic function f...

A: see below the answer and explanation

Q: W= x"+y+Z",

A: This is a problem of partial differentiation. Based on the general formula of PDE we will solve the ...

Q: If cotx 12 find the other trigonometric %3D functions

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Q: 6. ху\ + (1+х)y %3Dе*, у(1) — 0 7. sinx y'+2y cosx = sin2x, y : 2 6.

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Q: Question 2 If S(16x4 – 16x³ + 4x²)dx = F(x) + C, then F(x) 16 A 5 4 x3+4x4 3 B (4x² – 2x) 3 16 4 x3 ...

A: The given integral is 16x4-16x3+4x2.

Q: Find the differential equation whose solution is given by y? = 4ax ydx – 2xdy = 0 O ydy – 2xdx = 0

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Q: For the following function ds find the antiderivative s that satisfies the given condition. dt ds -=...

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Q: cot 2x J Tcot22x – 15

A: Given problem:-

Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1 + x 1 f(x) = 1 + + ...

A: Let's find.