Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter 'w' or -, as appropriate. If the limit does not otherwise exist, enter DNE.) if xs-1 im ), where f) - + a -x-2 if x>-1

Q: Find the Cartesian coordinates of the given point. (8, 0) 1) (0, 8) 2) (-8, 0) 3) (8, 0) 4) (0, -8)

A: Given problem:- Find the Cartesian coordinates of the given point.   (8,0)

Q: A business determines P(40) = 3000, %3D P'(x)0 where P(x) is the profit in thousands of dollars at a…

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Q: (3x-2)cx In the integration --17 what integration method is appropriate? a. Integration by Power…

A: Use integral methods

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 8 cos(t)i +3 sin(t)j +…

A: Solution is given below:

Q: : Triangle with points P(1,-1,2), Q(2,0,-1) and R(0,2,1), find: 1. Area of the triangle. 2. a unit…

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Q: Q9. Which of these is not the derivative of the function, y = x": A. -½x-1½ B. –0.5x-1Vx-1 C. –0.5 1…

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Q: calculate the flux of the vector field through the given surface F = zi + (y −1)j + 5xk, and S is…

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Q: 3x+2 dy for y = In, dx 2. Find Fully simplify your answer 3x-2

A: Solving the problem by finding the derivative.

Q: Find the arc length of the parametric curve. = 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T %3D

A: Use arc length formula

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

A: integration

Q: if x 2 valuate each of the following, if it exists. (If an answer does not exist, enter DNE.) lim…

A: Solution of given question is written in below steps.

Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x²…

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Q: [3 – 5i 2+41. L6 + 7i 1+8i! find the conjugate of its transpose. Given A =

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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

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Q: Exercise 1 A Write number sentences for the problem situations. Then solve the number sentences to…

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Q: Evaluate the indicated partial derivatives. z = 6a?y – 4a°y dz dz ду

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Q: x dx 2 /9 – 4x²

A: Using integration

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: Yz01003 b00 Cos07+3 2. 7) 300 Sing Y=0.002 Ysine dr do dø

A: A detailed solution is given below

Q: Find the mass and center of gravity of the lamina bounded by the x-axis, the line x = 49, and the…

A: Given problem:- Find the mass and center of gravity of the lamina bounded by the x-axis, the line x…

Q: 1. Find the solution to the system 4x - Зу +3z %3D 0 2х — Зу + 2z%3 0 бх — 12у + 7z 3D0.

A: “Since you have asked multiple Questions, we will solve the first question for you. If you want any…

Q: Find absolute maximum & absolute minimum f define on C0, 2]

A: maxima minima

Q: Determine the integral of sec^4 (x) tan^2 (x) dx * O 1/7 sec^7 (x) - 1/5 sec^5 (x) + C 1/3 tan^3 (x)…

A:

Q: Evaluate CF dralong the line segment C from P to Q. F= x j; P(3,2), Q(3,8) SCF dr- i

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Q: The exact area of the region enclosed by f(x) = -(x+ 2)(x-2) and g(x) = (r+ 2)(x- 2) is given by…

A:

Q: Solve for the Taylor series of the given function about the point x = 1. You can write the first 5…

A:

Q: Given the formula B V R, where statement B is true and statement R is False, the whole formula would…

A:

Q: dy 1. Find for the following: - dr f. 4x² - 9y² = 36 g. -+-=1 X y ... h. 3x°y+2xy² = 4 i. (3 - 2x) =…

A: f.4x2-9y2=36Differentiate w.r.t.x4×2x-9×2ydydx=08x-18ydydx=08x=18ydydxDivide18y on both…

Q: if x 2 a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.)…

A:

Q: Find g'(3) given that f(3) = -2, f'(3) = 4 , and g(x) = . 2x+1_ f(x) * Answer:

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Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

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Q: Consider the plane curve given by the parametric equations x = t + 22t – 23 y = t2 + 22t – 5 -- What…

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Q: Verify the formula LF a ds = S cdiv F dV in the Divergence Theorem by evaluating the surface…

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Q: Using any method, find the value of F. dr if F(1, у) — (бе" + ye")i + (e* + 5xe") j and at C :r(t) =…

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Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt the product directly and…

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Q: Ex: Show that if v, u, w are any vectors, then (H.W.) ux (v x w) + v x (w x u) +w x (u x v) = 0.

A: Dot Product Property :- a.b = b.a = a*b*cosθ

Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

A:

Q: 1

A: In game theory , the battle of the sexes ( BoS ) is a two player coordination game that also…

Q: Suppose the total revenue function is 4x? + 3x + 2. Find the average and marginal revenue. In…

A: Note:  In question 3, the function given is incorrect. So, i am solving the question 4. Question - 4…

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

A:

Q: Find the arc length L of the graph of r(t). r(t) = 12 cos(t)i+ 12 sin(t)j + tk, 0<t< 2n L= 75.66

A: arc length

Q: Use local linear approximation to estimate In(1.08)

A:

Q: Find the work done by the force field F(x, y, z) = xy i+ yzj+xzk on a particle that moves along the…

A: Solution is given below:

Q: A particle moves in a straight line with the given velocity v(t) = 24 – 6t (in m/s). Find the…

A:

Q: Question :44 A 240 mL pharmaceutical liquid suspension dosage form is settling at a rate of 4.8…

A: This is a problem related to divination concept. Based on the given rate and volume we will…

Q: 4. Evaluate: lim (a² + e-*)(= cac r) エー→0+

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Q: Identify the function, whose derivative is defined below: dy (х + h)2 — х2 lim h→0 dx h А. f(x) — Һ.…

A: Given dydx=limh→0(x+h)2-x2hWe know that the limit derivative formula is f'(x)=limh→0f(x+h)-f(x)h

Q: Evaluate the integral of the following using Miscellaneous Substitution 3. x /x*+ 1dx

A:

Q: The equations for free fall at the surfaces of Saturn and Jupiter (s in meters, t in seconds) are s…

A:

Q: 4. For the given function find the local extrema using the Second Derivative Test. f(x) = x³ – 9x2 +…

A: maxima minima