A slope field is given for a particular differential equation. Sketch the solution that passes through the point (0,−1).

Q: 2 Find the volume of the solid obtained by rotating the region bounded by y = x² , y = 0, and x = 3,…

A: we have to find the volume abouts y-axis

Q: The function f(x) = - 0.625x^3 + 16.789x^2 - 102.722x + 658.154 approximates the number of…

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Q: The region bounded by f(x) = −1x² + 6x + 27, x = 0, and y = 0 is rotated about the y-axis. Find the…

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Q: Sketch-the-graphs-x = 4y - y² and x = y

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Q: (a) Find the derivative of r(t) = (4 + t)i + tej + sin(5t) k. (b) Find the unit tangent vector at…

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Q: Find the absolute maximum and minimum of the function on the given domain. f(x,y)=2x² + 7y² on the…

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Q: Find the absolute maximum and minimum values of the following function over the indicated interval,…

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Q: We can represent planes using either vector equations or scalar equations. Which form do you think…

A: We have to answer which form of plane is better Either vector or scalar

Q: = Evaluate d5 dx5 [x³ − 3x + 1]. (a) (3x² - 3)5 (b) 0 (c) 72 (d) 6

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Q: 3. a) Find the limit of the sequence an = (2n²+3)(n-1) n(n² + 1)

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: sin 20x sin 21x dx =

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Q: Evaluate the integral. 6e6t ¹+12° +35 S- 12t dt

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Q: 5 The curve y = -5 x³ + x² + x + 1 "Trident of Newton". y 7 1 X 1 y= is known as the x³ + x² + x + 1…

A: To find the coordinates of the point where tangent to curve is parallel to y=2x.

Q: Find the dimensions of a rectangle (in m) with area 2,197 m² whose perimeter is as small as…

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Q: Assuming 6x³ - 2y² + 4xy = 0 defines y as a differentiable function of x, use the theorem dy = dx dy…

A: To find derivative at given point

Q: The perimeter of a rhombus is 68 inches and one of its diagonals measures 30 inches. Find the area…

A: Topic = Geometry

Q: -1 If ƒ(x) is a positive 1-1 function with inverse ƒ−¹(x) with f(a) = c and ƒ(b) = d then d π ñ ["°*…

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Q: Evaluate the integral. 2 2π π [ 0 0 0 sin z dx dy dz 2 2π π SS Sy sin 'sin zdxdydz =| 0 000 (Type an…

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Q: Find the derivative of the function. s = 8 t

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Q: differential equation dy/dx= 2^-x at the indicated point

A: Given  y'=2-x x y' 0 1 1 0.5 -1 2 2 4 -2 4 3 0.125 -3 8

Q: Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, and y = 0,…

A: Given: y = 4x2 x = 1  y = 0 about x-axis

Q: The area of an ellipse with axes of length 2a and 2b is лab. The percent change in the area when a…

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Q: Follow the steps below to find the nonnegative numbers x and y that satisfy the given requirements.…

A: Given  x + y = 160

Q: J xlnxdx X X

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: Find the slope at x = 3 on the graph of 2y - 4x = 9. (a) -4 (b) 2 (c) 10.5 (d) 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 4. Point of Diminishing Returns Assume that an advertising campaign is launched for a new product…

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Q: (b) Find parameters a and b such that the function jodonivi COS X f(x) = if if if x≤ 0 0 3 ax + b x²…

A: Given :

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

A: We need to change the integral into polar integral ∫0ln6∫0ln62-y2ex2+y2dxdy

Q: Find the derivative of the function at the given point in the direction of A. f(x,y) = -6x-9y,…

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Q: Find the centroid (x, y) of the region bounded by the two curves y = 6√ and y = 3 x = TU

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Q: Find the volume of a pyramid with height 28 and rectangular base with dimensions 5 and 7 using…

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Q: 3, 3, 1 > and b Let a = . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

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Q: Change the Cartesian integral - ² dy dx into an equivalent polar integral. Then evaluate the polar…

A: To change the Cartesian integral ∫-55∫025-x2 dy dx into an equivalent polar integral. Then to…

Q: Find the inverse Laplace transform L¯¹{F(s)} of the given function. 8s² - 49s + 294 s(s² +49) Your…

A: given  Fs=8 s2 - 49 s + 294s  s2 + 49 and asked to find the inverse laplace transform of F( s ).

Q: (a) Find the derivative. y = In(4x - dy dx (b) Find the derivative. y = ln ( 4x = dy dx 6) - 3 In(x)…

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Q: Find an equation of the tangent line to the curve at the point (1, 1). In(xex6) y = y =

A: The given equation is;  y=ln(xex^6).

Q: Consider the following problem: a box with an open top is to be constructed from a square piece of…

A: Note: There are multiple sub-questions. No specific question has been asked. So, We will solve the…

Q: Assume that x and y are differentiable functions of t. For the following, find dx/dt given that x =…

A: given  x2+y2=136d dx(xn)=nxn-1d dx(constant)=0

Q: Find the extreme values of f on the region described by the inequality. (If an answer does not…

A: Given, f(x, y) = e-xyRegion, x2 + 4y2 ≤ 1   Finding the critical points, ∂f∂x = -ye-xy∂f∂x = 0, y =…

Q: Find dy/dx at the given point without first solving for y. xy2 125 at (5, 5) d 11

A: The given equation is: xy2=125 Use the Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g'

Q: Consider the following vector function. Find each of the following. r'(t) = = r'(0) r(t) = cos(t) i…

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Q: Solve the differential equation. 2xy + 4x + (x² - 4) dy dx = 0 =

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Q: Find all local extreme values of the given function and identify each as a local maximum, local…

A: Topic:- Application of derivetive

Q: Find the derivative of the function at the given point in the direction of A. f(x,y,z)=2x-4y+7z,…

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Q: Find a) any critical values and b) any relative extrema. 3 g(x)= = -x + 3x-6 a) Select the correct…

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Q: 5) If f′(z) = e^z and f(0) = −3, find f (z).

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Q: Question 16 ( Find the slope of this line. Part 2- Full solution problems. A line with positive…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A: Given:-  The solid obtained by rotating the region in the first quadrant bounded by the curv x = 0,…

Q: Differentiate the function. f'(x) = f(x) = log₁0(x⁹ + 7)

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