Evaluate the following integrals by substitution. Show your complete solution. Express your answer in rational exponent. 3. ∫ √x^3 + x(3x^2 + 1)dx

Q: g expressions a. lim (2z - 1)(2-1)

A: Given : apply chain rule    find limit of about separately

Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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Q: Find the smallest value of x for which the series (x+ 124)" 2in(n) n 2 is conditionally convergent.…

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Q: Use the polygon law of addition to draw the resultant vector ( å + b) + ở for the following yectors.

A: The given vectors are added

Q: determine which statement is true {(x,y)|y=√9-4x2} (A) not a function (B) function; domain: [-3/2…

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Q: 3. Evaluate yn x dx

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Q: Let g(x) = | f(t) dt, where f is the function whose graph is shown. y f 4 4 20 (a) Evaluate g(0),…

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Q: Click an item in the list or group of pictures at the bottom of the problem and, holding the button…

A: Given problem:-

Q: A radar, using the polar coordinate system, detects that two airplanes are currently located at…

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Q: x³ +2x2-3x 2) Evaluate lim -6-1. x² +4x+3 X-3 Show every step.

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Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

A: A detailed solution is given below.

Q: QUESTION 1 Find ay/dx?- X = t + sint, y = t- cost

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Q: Find the angle between the diagonals of a cube

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Q: Given that ü = and i = and that üoi = 530 determine the value of the constant A. Yanıt:

A: This question is based on Dot product.

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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Q: Find an equation for the tangent plane to the surface given by f(x,y)=÷(4x² – 2y²) at the point…

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Q: A 42 cm piece of string whose length is given below is cut into two pieces. One piece is used to…

A: Here we have, A 42 cm piece of string whose length is given below is cut into two pieces. One piece…

Q: B: .A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (iv) a card of…

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Q: Vx-5 1) Evaluate lim 10. x25 X-25 Show every step.

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Q: 1. Use mathematical induction to prove the given statements below. 2 3+2 32+....+ 2· 3n-1 = 3" – 3…

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Q: 1. Jx cos 3x dx

A: Question 1 is solved. Solving more than 1 is against the policy.

Q: B: .A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (i) 2' of…

A: As per guidelines we can answer only three subparts questions at a time, if you need more answers…

Q: 7. Evaluate (5 – x)dA where R {(x, y) : 0 < x < 5,0 < y < 3}

A: Double integral

Q: Solve the linear differential equation dy y 2x2 dx

A: This ODE can be solved as follows:

Q: The MAIN use of Newton's Method is to: OFind the roots/zeros of a function O Find the derivative of…

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Q: f(Tn) f'(In). For the function f(x) = r- 2x 3. write Newton's formula as n 1 F(In) for solving f() =…

A: See the answer below

Q: 6. During the worst 4-hr period of a hurricane the wind velocity in miles per hour is given by v =…

A: The average value of the function is given by;0≤t≤4v(t)=1b-a ∫abv(t) dt     =14 ∫04(5t-t2+100) dt

Q: 7x + 4 if x 1 |

A: Here, the given function is: f(x)=7x+4, if x&lt;-2x2+1, if -2≤x&lt;12-3x if x=11-x+x if x&gt;1 where…

Q: In order to evaluate Vr2 – 10x + 29 dx, the correct substitution is Ox=-5+2 tan(t) Ox=2+5tan(t) Oa =…

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Q: In a trend that scientists attribute, at least in part, to global warming, a certain floating cap of…

A: Given problem:- In a trend that scientists attribute, at least in part, to global warming, a certain…

Q: 6. sin v- -2 cos Va + C %3D 4x2 1. Ja-8 dx = 18 (1-8x)4 (1-8x3)4 8. Se*dx =+ %3D In e

A: As per the instruction, we will be answering only the first three subparts. For (6),    ∫sinxxdxLet…

Q: Given, A = 2? zi – 2332j+ x} zk. ind divA at the point (1, –1, 1).

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Q: Let, \(f(x)=4x^2-12x+10\). Find: (a) the X- coordinate of all critical points, b) the open intervals…

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Q: Using the Optimization in Derivatives, solve the following problem: A 150-room hotel in Reno will…

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Q: Determine the absolute maximum and minimum values of the function f(x) = x'e* on the interval -1<x<…

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Q: B: .A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (iv) a card of…

A: We can answer both the question as below.

Q: 2. Find the area of the region bounded by the curve r = 2 cos 30 .

A: Given problem:- Find the area of the region bounded by the curve r = 2cos(3θ)

Q: Find the local linear approximation L (x) of the function f(æ) = 5 – a² at x= 2.

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Q: Given the three vectors å ,b and ở in 3D. The following question is t termine if operation involving…

A: We can solve this as follows:

Q: x2 – 3x – 2 if x 4 f(x) = V2x + 1

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Q: Determine whether the differential equation -dx = e* is x' +1 separable or not. If yes, solve it.

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Q: 5. Does the function f(x) = e2x - 2x have any points of inflection? Justify your answer.

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Q: Find dy/dx: 1. y= "(*++ dx 3 y = ," (x* + )

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Q: Find the nth derivative of y = In(16x2 – 9).

A: Given y=ln(16x2-9)

Q: Find the equation of the final function after all the following transformations have been made on y…

A: The below image has all the steps

Q: 9) Determine whether the series is absolutely convergent, conditionally (-1)"n convergent or…

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Q: -4 -3 Find the eigenvalues of matrix 6. 5 A. 1 & 2 B. -1 & 2 C. 1 & - 2 D. -1 & -2 E. None

A: Let's find.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(s) : (t…

A: I am attaching image so that you understand each and every step.

Q: determine which statement is true

A: Follow the procedure given below.

Q: Use trig substitution to evaluate: (hint: let x = 3tan0) %3D

A: ∫01xx2+9dx