Give the general form of the equation of the plane that is perpendicular to the plane x+2y x-4 1-2y z +5 and contains the line = -3.

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function, f(x)=x6-x3

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

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Q: 5) ( cos 'x dx -1 Where: u = cos(x) dv = dx

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Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1) b) has…

A: vector equation of line

Q: Find the area of the surface generated when the given curve just sayin revolved about the x-axis.…

A: SOLUTION-

Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: Find the area bounded by the curves -x + y² = 8, x = -2y and y = -2.

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Q: State the initial value theorem. Verify the theorem for the functions: (a) 3-4 sin t (b) (t-4)² and…

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

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Q: Show that the function f(x, y) = e2x cos(3y) satisfies the partial differential equation 4f + fyr =…

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Q: Jane is 2 mi offshore in a boat and wishes to reach a coastal village 6 mi down a straight shoreline…

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Q: (a) Find the exact area under the curve y = 1/x³ from x = 1 to x = t for t = 10, 100, and 1000. t =…

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Q: Find the area of the region bounded by y² = 4ax and x² = 4ay.

A: We have to find the area of the region bounded by y2=4ax and x2=4ay.

Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

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

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Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

A: The population of a town is decreasing at a rate proportional to its size.In 1980, the population…

Q: Let C be a curve with the parametric equations à = − ln(t + 1); y = sint, t = [0, 1]. a. Set-up the…

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Q: draw and identify the graph of the following surfaces a. z = √9-y²

A: Given

Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

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Q: Let f(x) = log2 (4x-x²)+2x. At what point is the tangent to the curve y = f(x) perpendicular to the…

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Q: the particular solution

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Q: ND THE AREA BOUNDED BY THE = x(x-1)², y-AXIS, AND THE =12

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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 volume of the solid generated by the region bounded by -x + y² = 8, x = -2y and y = -2…

A: We first sketch the region using a graphing calculator:   We can find the y-coordinates of the…

Q: Determine the center-radius Form of the equation of the sphere who diameter has endpoints at (2, -3,…

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

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

A:

Q: Find the volume generated by revolving the area bounded by x² - 4x - 4y + 4 = 0 and y = 1 about the…

A: To find the volume generated by revolving the area bounded by x2-4x-4y+4=0, and y=1, about the line…

Q: Find the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1)…

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Q: 1. The derivative of a constant is equal to A. -1 C. 1 B. 0 D. 2 2. If ƒ(x) = −5π, then ƒ'(x) is…

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Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

A: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

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Q: ds π Find a particular solution of =10csc² 2t determined by s= 2 when t = - dt

A: Given that the differential equation  ds/dt=10*csc^2(2t) Determine by s=2 when t=pai/4  To find the…

Q: dx x√x-1 dx √8+6x-9x² 3. S 4. S

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Q: In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Let's find initially present bacteria.

Q: If fx √1- x4 dx = ge ½ A B 0 C D) 1 H|2 H|4 g(e) de, then 9

A: We can solve the given integral by using substitution.

Q: 3 [*² [b³ – y³]² dy

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Q: Given: planes II₁ : 2x - 5y + z = −1 and II₂ : x + 5y + z = 5 intersecting on a line l (a) Compute…

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Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

Q: Determine whether each of the ff.differential equation is separable or not,if it is…

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Q: Given: parametric curve H defined by x(t) = tan¯¹t and y(t) = e¹t, where t € R (a) Find the slope of…

A: Given that parametric curve H defined by x(t) = tan-1t       and    y(t) = e4t , t ∈R           we…

Q: Find the slope of the tangent line to the graphof the polar equation 1 r = at Ø= 1-sinø 6

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Q: Given x = - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8

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Q: The rational expression A TRUE B FALSE 1 (9x² +16)² can still be decomposed.

A: this can not be decomposed. This statement is false.

Q: Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with symmetr…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 7. ydx-xdy + xydy = 0 Ans: In²+ y = c

A: We have to solve differential equations

Q: Given x = y³+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 B

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Q: True or false √2 If cosh x = V, then sinh x = 2. It is possible for a function to have an absolute…

A: To determine whether the following statements are True or False.1 If cosh x=62, then sinh x=22.2 It…

Q: Given: vector-valued function R(t) whose derivative R' (t) = (4t, 6t, -12t) (b) Reparametrize R…

A: Let's reparameterize vector value function R(t).

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: In x Compute -dx. 3√√/x 9 X 3 A²x²0 nx-x²²+ C A.- In 2/3 2 4 1 B.- - +C X 3 4/3 4 3 C.--(In x)x-4/3…

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