Use the given the function: (z+2)(x-3) f(x) = (x+1)²(x-2) to answer all of the questions below.

Q: Consider the function. x-7 f(x) x-6 Step 1 of 2: Find all values of x that correspond to horizontal…

A: solution:-f(x)=x-7x-6f'(x)=x-6ddxx-7-x-7ddxx-6x-62f'(x)=x-6-x-7x-62f'(x)=1x-62,     x≠6for…

Q: Find (au/ay), at the point (u,v) =(√2,3), if x = u² + v² and y= uv. ди (2) = (Simplify your answer.)…

A: Given query is to find indicated partial derivative.

Q: Find the indefinite integral. 1 dx 3 (x²+9) 2 a. b. C. d. x² 9√x²+9 +C +C 9√√x² +9 x 9√√x² +9 x² +C…

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Q: Set-up the integral using horizontal element for the volume of the solid obtained by rotating the…

A: We have to find volume about y=-1

Q: 9) (x - 2)² 16 9 (x+5)² ¸ (v+3)² _ 1 = + 25 16 +(y-1)² = 1 11) 2 x² X 13) 121

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Q: Set-up the integral using vertical element for the volume of the solid obtained by rotating the…

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Q: 5 Given cos(8): and the terminal side of 8 lies on the fourth quadrant. What is the value of…

A: Given problem:- Given cos(θ)= and the terminal side of e lies on the fourth quadrant. What is the…

Q: Find all solutions to the given equation. In the choices, k runs through all integers. √3csc(x)+2=0…

A: We can find the answer as below.

Q: t 2 If the velocity of a moving object is y(t) = --- 2 12 in meters per second, then what is its…

A: The veloctiy of a moving objcet is v(t)=t2-2t2 in meters per second.

Q: 6. A curve which intersects some straight line in an infinity of points (but for which not every…

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Q: 3. A function g(x) is a probability density function function g(x) = -&- 5z 5e is a probability…

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Q: Find the area of the plane region bounded by y=-x+2 and y=x²-2x

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Q: w Dy ),-0 7 By b. Əw əz C. aw əz

A:

Q: A train is starting at noon travels north at 40mph. Another train starting from the same point at 2…

A: Let's find speed of trains at 3 pm.

Q: If f(w) = e f'(w) = sin w+ 4 cos w find f'(w). Use exact values. J

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Q: If f(x) = f'(x) = 1 COS :−¹(5x²), find f'(x). Use exact values.

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Q: 3 s cos³x + 8sin x cos²x 20652x basin ²x dx;cosx 0

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Q: dx √x-3√x X ffv)dy, find fly)

A: solution:-∫64729dxx-x3dx=∫64729dxx12-x13dxlet x=y6 or y=x1/6x=64,     y=641/6=2x=729,…

Q: 4) x² (1-8)² + 100 25 =1

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Q: a point of intersection on the unit circle whose x coordinate (3/3₁-3) (-/-/-/-) 5'5 2√6)

A: Given query is to find the intersection point.

Q: 8. A box is to be made with an open top from a sheet of cardboard by cutting four equal squares out…

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Q: 19) Evaluate the double integral for f(x, y) = 2y+x over the rectangle region R defined by 3 ≤ x ≤ 4…

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Q: Use the Limit Comparison Test for 00 10n² + 16 Σ an = Σ n(n - 12)(n-12) n=21 n=21 to prove…

A: Solve the following

Q: THE AREA BETWEEN THE CURVES 2 4y = x² AND Y²³ = 4X 15 REVOLED ABOUT THE LINE X= -1. SOLVE FOR THE…

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Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a horizontal element, the total…

A: Follow the procedure given below.

Q: The velocity (meters/second) of an object at time / seconds is governed by the IVP: 1 dv k dt + v =…

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Q: Let u(x) = sin(x) and v(x) = x¹0 and f(x) 10 - u'(T) v'(x) u'v – uv' f' = V² = II u(x) v(T)

A: We have to solve the derivative

Q: Q2/ The region bounded by the curve y = x² and the line y = 3x, in the first quadrant is revolved…

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Q: 3. Let R(t) = (t²,1 — t², t) and r(t) = cost. Determine the parametric equations of the line tangent…

A: Given

Q: f(x) = x³, y = 1, x=1 Find the volume of the solid obtained by rotating the region B about the…

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Q: Find the area of the plane region, 0≤x≤ π²-4 S.U. 4 1.111 s.u. 1 s.u. 2 S.U. bounded by y=sin X. X =…

A: This question can be solved using the concept of area under curves.

Q: Using Rationalizing Substitution S O Arctan(y) + C Ⓒ2Arctan(y) + C O In(y) + C O2ln(y) + C dx X√√x-1…

A: The integral is  ∫ dxxx-1=∫f(y)dy

Q: Find the derivative of the following functions: tan (2x²-1) 1. f(x) = sin(2x²-1) 2. f(x) = sin² 4x…

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Q: Evaluate the given integral as indicated: Use Integration by Trigonometric Substitution x³ dx 5 (4x²…

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Q: Sketch the graph of the funcuon f(x) = 2x-3 x2-4

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Q: The graph of a derivative f' is shown to the right. Use the information in the graph to determine…

A: The graph of the f'(x) is given as

Q: Let ƒ(x) = (cos( − 4x – 5)) (sin(6x − 2)). Then ƒ'(x) =

A: f(x)=(cos(-4x-5))(sin(6x-2))

Q: The formula for solving for the area in the first quadrant bounded by y = x², the circle x² + y² =…

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Q: Find all solutions to cos(70) cos(p) = sin(40) on 0 ≤ ø Give your answers as a list separated by…

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Q: Solve the Indefinite Integral. xe²t S dx (2x+1)² A [1-21] +0 e2x 2x C 4 2x+1 B. 2-2(22+1) + C 4 C.…

A: SOLUTION-

Q: dy dx 4x + y 2x+y

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Q: 4- Find the question of the that is tangent to the curve y=-3 cos2x at x= π/6. Express with exact…

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Q: ODE  Solve the homogeneous equation  dy/dx = x+3y/x-y

A: Use the homogeneous differential equation and simplify it

Q: dx Using Rationalizing Substitution S- -=Sf(y)dy, find ff(y)dy- X√√x-1

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Q: 1. f(x, y) = 4x² + 2y² + 5 subject to the constraint x² + y² - 2y = 0

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Q: dentify the graph _____ A. hyperboloid of one sheet parallel to x-axis B. hyperboloid of 2 sheets…

A: answer is in next step. please give a like !!

Q: Determine the derivative of the following imp of paper, assuming that it is differentiable.

A: given is x+y3=2c(xy4)differentiating both side with respect to xdxdx+dy3dx=d(2c(xy4))dxusing product…

Q: The graph of y = f(x) is given. 6- 5 4 3 2 6-5-4-3 -2 -1 -3 -4 -6- 1 2 3 4 5 6 a

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Q: If w = 2x² + 2y + 2z+ cost and x+y=t, find the partial derivatives below. G. (22) X.X C. a. (W) b.…

A: Note : As per our guidelines we are supposed to answer only first 3 subparts if there are multiple…

Q: Find the area of the plane region bounded by y=-x+2 and y=x²-2x 07 s.u. 9 9 s.u. 01 S.U. 2 S.U.

A: