Question 6 6dx For the method of partial fractions, to evaluate S90 -1 = S Adx + S = X-1 Bdx X+1' the values of A and B are

Q: d/dx(arctanh(2x)) 2XIn2 A. 1-4X 2x B.- 1-4X 2 In2 C. 1+2x 2x D.- 1-2x

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Q: 5. Suppose f is continuous on [2, 8]. Use the table of values of f to f(x) dx using a left, right,…

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Q: Determine the value of x when the slope is its maximum for the function f(x)=2cos(3x)

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Q: 6. Determine the Cartesian (scalar) equation of the plane that... a) contains the points (6,1,0) and…

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Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: I have shaded the area green which is to be calculated

Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

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Q: Find the volume of the solid generated by the region bounded by x² + y = 6, y = x, y = -2 and x = -2…

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Q: Find the area of the region in the first quadrant bounded by the curve y = √x² + 5, the x-axis and…

A: Given: y=x2+5 Graph of the functions given are

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: We first graph x2+y2-6y=0 and y=6-x using a graphing calculator.  The shaded region will rotate…

Q: closed box with a square base is to contain 252 cubic feet. The bottom costs $5 per square ot, the…

A: Please refer to the image below

Q: If z is a function of x and y implicitly defined by əz əz find and əx ду at (x, y, z) = (0, 2, -1).…

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Q: A rectangular field having an area of 2500m² is to be enclosed by a fence, and two additional fence…

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Q: = Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x)…

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Q: The limit below represents the slope of a curve y = f(x) at the point (a,f(a)). Determine the…

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Q: Differentiate the function: y = e-x cos²x x²+x+1

A: To differentiate the function.

Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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Q: 6. If y = 3√x, then what is y'? 2 A. y' == x 3 B. y' = 2/2 x3 C. y' = 1/ x3 D. y' = ¹/2 x 3

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Q: 112 points/ Use algebraic techniques to determine whether the following function is even, odd, or…

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Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0 ≤ x ≤ 1

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Q: Please answer both

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Q: Show that the three functions: f₁(x) = ex-8f₂(x) = exf3(x) = 4(2x-2) are linearly dependent.

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Q: 2. z = x + 2 У Х x

A: Solution

Q: Solve the first order linear ordinary differential equation x sin x dy dx + (sin x + x cos x) y =…

A: Here, the given DE can be written as: xsin xdydx+(sin x+x cos x)y=xex⇒dydx+sin x+x cos xxsin…

Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x-2).

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Q: 26 Find the value of k so that line 4, 2]-[2-20]++ [2, k₁-3) is parallel to the Plane *x+24-42=12

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Q: 3 [*² [b³ – y³]² dy

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Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: I have shaded the area green which is to be calculated

Q: Evaluate the following integrals. -1 L₁ (3²- (3x² - 4x−¹+2) dx

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Q: Calculate the average rate of change for the function f(x) over the interval-1≤x≤3

A: Topic = Algebra

Q: In an autocatalytic chemical reaction, the product form is a catalyst for the reaction. If Qo is the…

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Q: Find the height of a circular cylinder of max. volume that can be cut from a spherical wood of…

A: using double derivative test to find out height when cylinder volume would be maximum.

Q: dy Find the complete solution of 2e-2 cosx-sin²x = 0. dx Note: [e"du=e" + C

A: The given differential equation is 2e-2y cos x-dydx sin2x=0⇒dydx sin2x=2e-2y cos x⇒dy2e-2y= cos x…

Q: The selling price P of an item is 100- 0.02x dollars, where x is the number of items produced per…

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Q: Pls show complete solution (c) Set up the integral which yields the area of the indicated region R…

A: We need to setup integral for area.

Q: For the following exercises, find aj dt and direct substitution. 226. f(x, y) = x¹, x=t, y=t using…

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Q: 2. Determine whether each of the following series converges or diverges. 5n - 2n (2) Σ 3n+4n n=0 +∞o…

A: Given

Q: = 0 and y 16k (x-3) = 0. Find the area bounded by the parabolas (x - 3)² - 16ky =

A: Given: (x−3)2−16ky=0 and y2−16k(x−3)=0 Graph of the given curves will be as follows

Q: P N

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Q: The curve defined by R(g) = 1. Considering f(g) to be a function such that f (1) = 0 and f' (1) =3.…

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Q: Given x = y²+2y 8 - In(y + 1), find the arc length for 0 ≤ y ≤ 3

A: Given: x=y2+2y8-ln(y+1) The arc length is: L=∫ab1+dxdy2dy Now, dxdy=dy2+2y8-ln(y+1)dy…

Q: Evaluate the following integrals. 13 1 sin²x -dx

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Q: [xv x√2x + 1 dx

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Q: What is the inverse for the function f(x) = 2+3/1-x? A. f1(x)=1-(x-2)³ 1 B. f¯¹(x) = 2+³/1-x C.…

A: Given that:  f(x)= 2+ (1-x)1/3 and we find the value of f-1(x).   Here i attached the solution of…

Q: Solve ₂(x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

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Q: Find the orthogonal trajectories of the given family of curves. 1. y = c (sec x + tan x )

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Q: The curve y area. = √x + 2 is revolved about the y-axis from x = 1 to x = 8, find the surface

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Q: Advar Ex: If w = f(x,y,z), x=x(r,0), y =y(r, 0), z = z(r, 0), find wr, we? дw dz aw ax дw ду aw

A: We will use chain rule to solve this question.

Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: Find the derivative of f(x) = ✔ (6x¹ + x² − 1) 5.

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