Ex: If f(3) = 0, show that əz дz x- x² + y = Z. (H.W.) əx Əy

Q: ds Find the complete solution of = 8t³ √s. dt

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Q: rve (y+1)2 = 4x3 from x=0 to x=1? (4) =q8

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Q: Two vehicles start out traveling side by side along a straight road. Their position functions, shown…

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Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: a. Use the definition mtan = lim f(a+h)-f(a) h h→0 b. Determine an equation of the tangent line at…

A: Please refer to the image below

Q: If 10 ["f(x) dx = 17 and A True B) False f'se f(x) dx = 12, then 10 f(x) dx=5

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Q: 8. An arithmetic sequence has the 5th term equal to -64 and the 14th term equal to - 1. Calculate…

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Q: a.) Solve the equation z³ − 1 = 0 15 1 √3 b.) Evaluate (-+-+3) " 2 2

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Q: By method of Integration by Partial Fractions, A B(2x-2) + C (x³+5x²+6)dx (x²–2x+5)² = √ [₁²-2² +…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Given x = ; ș¹²+2y — In(y + 1), find the arc length for 0 ≤ y ≤3 8

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Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: Let P be the point with Cartesian coordinates (6,9), and C be the plane curve with parametric…

A: The parametric equation,x=t2-t and y=2t3-1123

Q: Let line 1: x = = = and point P(1,0,1). 2 ● Find the set of parametric equations of the line…

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Q: [₂7-4x dx -2 Determine the value of [4f(x) dx given that [ƒ(x) dx = 10 and ſº ƒ (x) dx = 3. 27 sin…

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

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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: Find Vector A and B such that A is parallel to , B is perpendicular to and A + B =

A: We have to find vectors A and B such that A is parallel to 2, 1,-1, B is perpendicular to 2, 1,-1…

Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy +…

A: We have to find the general solution of the given differential equation using variation of…

Q: Solve y at x=1. dy/dx - 2(x+1)^3 = 4y/(x+1)

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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: 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: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

A: The function is given by y = x2sinx+xcosx-2sinx To evaluate: The first derivative of the function.

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

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Q: 2x fe²x sinx dx

A: Using integration by part.

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

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

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Q: z = xey + y ex

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Integrate the following: 1. f xdx x²-x+1

A: The given integral is x/(x2-x+1). Repost the next question.

Q: The most convenient way to evaluate A) True B False 2x-3 S- -dx is use Integration by Parts. x²-3x+5

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Q: Give the general form of the equation of the plane that is perpendicular to the plane x+2y x-4 1-2y…

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Q: Solve the differential equation using inspection method d'y d³y = 24. dx5 dx³

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Q: ds Find the complete solution of = 8t³√√s. dt

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Q: x² - 25 to fill in the table: Xx - 5 6 5.5 5.1 5.01 Based on ONLY the table of values above, what…

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Q: T/6 3 coss 3x dx

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Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 Cos 0 Er = g(0) = 12/250c4 D:r=3 (1.) Show…

A: Let's solve part 3 and 4.

Q: If 2x²+x+1 S (x-1)(x+1)(x-2) A -2 B None 11 3 U D E - 3 11 3 A SA -dx = B + x-1 x+1 x-2 с -+ dx,…

A: Given, 2x2+x+1x-1x+1x-2

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: Find the inverse of 2=2-51.

A: Here, we need to find the inverse of z = 2-5i. So,…

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

A: The first question has been solved as per the request of the student.     The center radius form of…

Q: 27 3. Explain how you would find the general term of the sequence: 4, -6, 9, - ".

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Q: The gradient of a curve is dy/dx + (x^2)/2 = 3x. Find the equation of the curve if it passes through…

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Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

A: Given

Q: (ii) tank (In x) = x²-1 x² +1

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Q: (b) p = 2 sin p cos 0

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Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

A: Given x→=2i→-3k→ & y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: Evaluation. 1. Determine the antiderivative for each. Show complete solution. √ 5x³=3 dx 2. √(√x√x +…

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

A: Solved below.