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

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: 7) x¹ 9-x ² dx X 3 2 2 where u-x ² dv = x √ 9-x² dx 2

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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: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

A: Solution :Without odd-even…

Q: Find the transition points. y = 5x³ + 120x² (Use symbolic notation and fractions where needed. Give…

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

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Q: f(x)=8x¹-7x³+2 on [−2,1]

A: To compute the average value of the given function f(x)=8x4-7x3+2 on [-2, 1]

Q: Given: planes ¹: 2x - 5y+z=-1 and 2: x + 5y+z=5 intersecting on a line . (a) Determine the symmetric…

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Q: R(t) is a differentiable vector function for t > −1 with R' (t) = (1/1/² ,1 + t²) and R(0) =…

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Q: smaller x-value larger x-value (x, y) = (x, y) = X X

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Q: (ii) tank (In x) = x²-1 x² +1

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

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Q: y x3 - 2x*-5x + 2

A: Second Derivative Test : Consider the given function f(x) .Find Critical point , f'(x)=0 (say) 'c'…

Q: a. On a rectangular cartesian coordinate system, sketch the parallelepiped having the vertices (1,…

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Q: dy Find by implicit differentiation, given that x²y – 2y6 = =-5. Your answer could involve both dx x…

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Q: A product can be produced at a total cost of C(x) = 500 + 100x² + x³ dollars, where x is the number…

A: Solved below.

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: Consider the function. x³ + 12 f(x) = X Determine the intervals on which f is increasing,…

A: A function f (x) is increasing on the interval I if f'(x) >0 for x in I. A function f (x) is…

Q: 3 S ₁² √ (²√₁² - ²√+²) ³ dt

A: Given

Q: Given: planes Π1 : 2x − 5y + z = −1 and Π2 : x + 5y + z = 5 intersecting on a line ℓ. (a) Compute…

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Q: Convert the Cartesian coordinate (-5,-3) to polar coordinates, 0≤ r = 0 = Il

A: We have to find polar form

Q: 4. u = xz siny + yz cosx + xy tanz

A: Given,  u=xz sin y+yz cos x+xy tan z

Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

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

A: To differentiate the function.

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

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Q: Find the transition points. f(x) = x(17x)1/3 (Use symbolic notation and fractions where needed. Give…

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Q: Find the derivative of f (y) = 153/g In(y)

A: Given: f(y)=15y3lny

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

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Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂ : r = 2-2 sin (in red) and let R be the…

A: Let's solve. Two curves given r=3 and  r=2-2sin(theta).

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

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

Q: 4. Determine the number of terms in the sequence: -45, -32, -19, -6, 410 ***

A: There are 36 terms  in the sequence.

Q: A B C d Using integration by parts, Then k is? (a)-1.5136 5²x² ²x³ cos (x²) dx = k - S²x - [*x…

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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: Compute 4 sin(TTX) d dx A. 4 sin(TTX) B. 4sin(TTX) In4 C. 4sin(x) (πIn4).cos(TTX) D. 4 sin(TTX)…

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Q: Find the volume generated by revolving about the y-axis the area bounded by y2= x-2, y=x-4 Use shell…

A: Here we have to find the volume by using shell method.

Q: Find the Area of the Surface obtained by rotating the curve about the y y = √√x, 1 ≤ y ≤2

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

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Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: ∫-22(x+1)(x2+2)2(x2-1) dx

Q: True or false Unlike the anglet in the trigonometric function cost, the t in the cosht represents an…

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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: z is a function of x and y implicitly defined by Find and i at (x, y, z) = (0, 2, -1) əz Əx Əy y³…

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Q: 1. Write the polar form of the following complex number Z = 3

A: We know that polar form of complex number z=x+iy is z=r(cosθ+isinθ) Where r=x2+y2θ=tan-1(yx)

Q: 3- Air at 25°C and 100 kPa at a relative humidity of 75 percent. The parti pressure of water vapour…

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Q: 9 Determine the area to the right of g (y) = y² +4y-5 and to the left of the y-axis.

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

A: Here we have to use the concept of derivatives.

Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

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Q: Use the slopes of tangents to determine whether the function f(x) = -6x²+36x is increasing,…

A: The given function f(x)=-6x2+36x at the point x=4.

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

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Q: Find a particular solution of =(x−1)² if y=-21 when x=-3. dx

A: dydx  = ( x - 1 )2   , y = -21, x = -3 we have to find particular solution of it

Q: y = (x² + 2)(x-3)

A: The objective is to find the derivative.