1) Find the domain of the function f(x) = √3-x x+4

Q: 10 π/2 sin1/5 0 cos Ꮎ dᎾ

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,2) on the surface…

A: Let fx,y,z=2x2+3y2+z2-9 Gradient vector ∇fx,y,z=fxx,y,z,fyx,y,z,fzx,y,z

Q: Find fx(x,y) and fy(x,y). Then, find fx (2,- 4) and fy (-4,4). f(x,y) = 4x cos (лу) fx(x,y)= (Type…

A: Implicit differentiation is done and then values of x and y are substituted.

Q: Find an equation for the plane that is tangent to the surface z = In (x + y²) at the point P(0,1,0).…

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Q: BOTTOM LINE QUESTION Find the exact area under the curve f(x)=x²e* from x=0 to x=2. Show your work…

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

Q: Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.) r = 7 +…

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Q: Set up, but do not evaluate, an integral for the length of the curve. x = 7 sin(y), osys. 1. (C dy 2

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Q: af af 6. Find and where f(x,y)=√√/24 - x² - 2y². Interpret the value of fx (2, 2) in əx ду two ways…

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Q: 5. Suppose a novelty cake has a base which can be described as the region bounded by y = 4x² and y=…

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Q: Find the partial derivatives of the function dw Or dw dw Ot W= √√2r² +58² +4t²

A: We can find the partial derivative of the function .

Q: A bacteria culture started with 8500 bacteria and increased by 35% in the first 2 hours. (a) Find…

A: Let Q(t) be number of bacteria at time t ⇒Q0=8500 initial number of bacteria

Q: Given the polynomial y = 3x³ +21x² +31x + 2, • list the possible rational roots: 2 2 1,-1,-1,- 2,-2,…

A: The given polynomial y=3x3+21x2+31x+2 We have to find the all possible rational roots of the…

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=4f(x)+5x. If the…

A: Using derivative

Q: Determine where the graph of f(x) = 2x³ + 27x² − 45x-60 is concave down. f(x) is concave down where…

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Q: {2, y) = tans (2 I

A: Please see the below picture for detailed solution.

Q: 2. Given r(t) = (2, e³t-3, 6t+2) with r(1) = (2, 1, 7) and r'(1) = (2,0, 5), find r(t).

A: The objective is to find r(t).

Q: If f(x) = In(x) +6 find f'(1).

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Q: Find the equation of the line tangent to the curve x4 + 4y4 = 5 at the point (1, 1).

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Q: Let f(x,y) = (- (x+y))8. Then 02f дхду Ꭷf Әхдудх 23f дх2ду

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

Q: 01 O-3 O 733 113 It is known that function f is an increasing function that satisfies f(1) = −3 and…

A: Given:      f1=-3      f-11=3 we know that       f-1'y=1f'x

Q: Find the equation of the line tangent to the curve 8x4 + 8y² = 16 at the point (1, 1).

A: To find the equation of the line tangent to the curve 8x4+8y2=16 at the point 1, 1.

Q: Find the transform of the given function by use of a table. f(t)=e-4 4 A F(s) = 5(₁-4) 1 s+4 B F(s)…

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Q: Solve the differential equation. y' − y = 9ex

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: x² 421875 For the given cost function C(x) = 54√√x + a) The cost at the production level 1700 b) The…

A: Note:- These are multiple sub parts but we can solve max 3 sub parts so i am solving here first 3…

Q: Find the exact arc length of the curve over the stated interval. 1 1 x==y+y from y = 1 to y = 2…

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Q: Use the graph to locate the absolute extrema (if they exist) of the function on the given interval.…

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Q: If f(x) f"(2) = x2 4 + X find ƒ”(2). x

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Q: du Evaluate at (x,y,z)=(4,3,0) for the function u(p,q,r) = e Pacos(r); p = = = ²1/₁, q=x² Iny, r=z.…

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Q: Given f(x, y) = ry - 6zy. Compute: 8²f dz² 8²f dy²

A: Topic = Derivative

Q: Prove that the following differential equation: (1 + x2)y'' + 2xy' - 2y = 0 has the following…

A: To prove that y is solution of a differential equation then we just substitute the value of y' and…

Q: Using the same graph of f(x), what is lim f(x)? X→ 4 AN 2 3 -1- -2+ 4 1 doesn't exist

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Q: 16. cosh (x + y) = cosh x cosh y + sinh x sinh y

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Q: Write the function below in the form y = f(u) and u = g(x), then find y = cos (csc x) What are the…

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Q: A particle moves along the x-axis so that at time t 0 its position is given by x(t) = −t² − 2t + 35.…

A: solution:-particle's positionx(t)=-t2-2t+35where t≥0particle velocityv=ddtx(t)=ddt-t2-2t+35v=-2t-2

Q: Find the limit (enter 'DNE' if the limit does not exist) 1) Along the x-axis: 2) Along the y-axis:…

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Q: Evaluate the triple integral E 2x dV where E = {(x, y, z)/0 ≤ y ≤ 2,0 ≤ x ≤ √4-y²,0 ≤ z≤y}

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Q: A function f (x) is continuous at x = a if: 1.a is in the domain of f (x) II. lim f(x) exists x→a…

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Q: 3. (a) Find the Laplace transform of (i) f(t)=17te-2-3 sin(9t) (ii) fo

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Use implicit differentiation to find y² + 4x³ = 8y - 5x² dy dz z(5+6x) y-4 da X

A: Topic = Derivative

Q: | r - 1 dr

A: To evaluate the given integral.

Q: limx→4 x²-4x √I-2 ||

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Q: A rectangular box is to have a square base and a volume of 81 ft3. If the material for the base…

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Q: 2-x 2 +5 1 dx

A: Given, ∫2-xx2+5xdx

Q: Given the table of values for f(t), is f(t) increasing or decreasing? It f(t) 1 10 O increasing O…

A: To determine whether the given function is increasing or decreasing.

Q: Give your answer in interval notation. Determine the intervals where the graph of f(x)=x²-3x²+x-1 is…

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Q: 2 16. xy = √√x² + y²

A: Given Equation:- xy=x2+y2

Q: Consider the function f(x) 72x² + 10, The absolute maximum of f(x) (on the given interval) is at X =…

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Q: 6 √√√m² +2+m6dm

A: Concept: Power rule of the integration ∫xndx=xn+1n+1+C Where C is constant

Q: -3 2. Express z³+z' (the conjugate of z raised to the third power) in polar coordinated form u(r,0)…

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Q: 2x² + 4 over the interval [-2, 1]. Enter an exact answer. If there is more than one value of x in…

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