2. Explain how we know the function f(x)= 2.x is one-to one. Then find the inverse function f. x- 3

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Q: A trough is 3 m long, 5 m wide, and 4 m deep. The vertical cross-section of the trough parallel to a...

A: Find your answer below 

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A: As we know that; The expression for the length of the vector-valued curve; L=∫abdxtdt2+dytdt2+dztdt2...

Q: 2 3+1 (z2 + 4 )? dx. Which of the following is equal to the given integral? O x 3 +1 = Aæ + Ba? + ( ...

A: given I =∫ x3+1x2+42dxf(x) = x3+1x2+42by method of partial fractions f(x) can be written as\x3+1x2+4...

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Q: -6/- -70 -8 Provide your answer below: lim f(x) = U a. x -4 b. lim f(x) =D | x-4+

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Q: Find the derivative as indicated: 1) y = 3 cos x + 2 sin x ; find y' %3D 2) f(t) t sint ; find f'()

A: Given: 1: y=3cosx+2sinx2: f(t)=t sint   To Find: 1: y'2:f'(3π2)    

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A: We have to find equation of tangent line and normal line

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A: Note: As there are two different questions in the picture we will solve the first question by defaul...

Q: Use substitution to evaluate the integral 6 cos t (2+ sin t)? dc 6 3 3 + C 2+ sin t + C 2+ sin t + C...

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Q: 3 -dx 4 - x

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Q: 4. The height h (in metres) of a certain section of a roller coaster is modelled by the equation h(x...

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Q: Find the indefinite integral. 4x2+2x-1 d.x none of these Omz + 1| -31m|z미-글+C o+ Inz* + =*|+C In a+1...

A: Given: I=∫4x2+2x-1x3+x2dx   We know that; The Power rule: ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And ∫1ax+bdx...

Q: How to convert a cosecant theta to tangent data

A: sinθ = 1cosecθ  and cosecθ = 1sinθ

Q: solve the differential equation: y(2xy+1)dx+x(1+2xy-x3y3)dy=o

A: Given diffrancial equation y2xy+1dx+x1+2xy-x3y3dy=0Solution :y2xy+1dx+x1+2xy-x3y3dy=02xy2dx+ydx+xdy+...

Q: Please answer the question below: 1.) Explain why the integral below is an improper integral and wha...

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Q: What is the y-intercept of the function y = cot I? || ㅇ(T,0) O (0,0) O (1,0) (0, 1) O It does not ha...

A: The function is given as y=cot(x) The objective is to find the y-intercept.

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A: In this question we will use basic concepts of calculus i.e concepts of indefinite integration. We w...

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Q: PART - B IA. Solve (4xy + 3y? - x)dx + x(x +2y)dy = 0 with y(2)=2. IB. Solve (x²D2 + xD - 1)y =ri

A: Since, you have posted multiple questions. As per guidelines we will solve only first question. If w...

Q: 1. Find the second derivative of the function. 8(x) = 3\/x + e7*In(x)

A:

Q: Time Interval [1, 2) [1, 1.5] [1, 1.1] [1, 1.01] [1, 1.001] Average Velocity | Complete the followin...

A: We will find the average and instantaneous velocity. 

Q: 1. Evaluate the following limits. x+ Vr - 3r а. lim Vr4 + 3x

A: We have to find limit

Q: 8. Compute the derivative of the following equation. (1) y = (x +1)3(2x – 2)2 (ii) y2-4x² y+x=16

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Q: What are the coordinates of the vertices of the hyperbola whose equation is given by 4y2 – x² = 4? A...

A: The given hyperbola equation,        4y2-x2=4

Q: The least squares equation, y= 18.9476+1.1842x. If y= 66.3156, what is the value of x? *

A: On solving this we will get

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Q: A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure belo...

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Q: dy find dx t - 1 If y = t and æ = t+1 dy A. 2t(t + 1)2 dx В. dy = t(t+1)² dx dy 2t С. dx (t + 1)? dy...

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Q: Problem 1. Draw a direction field for the given differential equation. By hand, sketch an approxi- m...

A: Solutionn is here

Q: Give the coordinates of the vertex to the right of the center in the equation: (x- 3)2 (y-1)² =1. 9....

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Q: 6. Let T: R → R be defined by T((a, b,c)) = (a, a – b,b + c). Determine whether T is a linear transf...

A: 6. T:ℝ3→ℝ3 be defined by Ta,b,c=a, a-b, b+c

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Q: r(t) = ln(13 – t) i+ v9+tj- 3e¯t k t) = (

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

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Q: х — 3 (x+ 2) (x – 1)²

A: The given integral is; (x-3)/[(x+2)(x-1)2].

Q: JUIR tO JusLily your aASWers. Witë your solutions properly, heatly, and carefully answers as much as...

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Q: 12

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Q: In the decomposition a = aTT + aNN, what do aT and aN represent?

A: Solution: Given data, a = aTT + aNN

Q: Use Simpson's Rule and n = 4 to find an approximation for the definite integral Vr +1 dr.

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Q: Use a finite sum to estimate the average value of f(x)=x* on [0,2] by partitioning the interval into...

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Q: Graph the function y = 9 – 3cos(50rt) without a calculator starting at t = 0.

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given point...

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Q: Evaluate the following definite integrals, t(1 -t)² dt = а.

A: Solution: ∫-11t(1-t)2dt Expand=∫-11t-2t2+t3dt

Q: det a det C

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Q: 2. Viola drives 170 meters up a hill that makes an angle of 6° with the horizontal. To the nearest t...

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