10. 1 -3-3x 3-3x-у 15. 0 J0 Т 0 dz dy dx

Q: Use implicit differentiation to find dy/dx. 14) xy + x = 2

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Q: Solve the initial value problem. dy 27) dx = x(6+x²)²₁ y(0) = 0

A: Given query is to solve the differential equation.

Q: Use a finite approximation to estimate the area under the graph of the given function on the stated…

A: Given f(x)=x2   We are required to findThe area under the curve f(x)=x2 between x=4 and x=8 using…

Q: Calculate the slope of the tangent to the curve of the following formulas: y = -x + 6x + (x + 9)² at…

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Q: Use implicit differentiation to find dy/dx in terms of x and y: x - 3y = 2xy

A: Differentiate

Q: Find the vertex, focus, and directrix of the parabola x² +12y = 0.

A: The given equation is x2+12y=0

Q: Find the area under the given curve over the indicated interval. y=x²: [2,3] The area under the…

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Q: Find the most general antiderivative. 23) (6x3+3x+5) dx

A: 23) The given integration is: ∫6x3+3x+5dx  To find the most general antiderivative.

Q: 2. Find the degree 3 Taylor polynomial of f(x) centered at r=0 = X (1+x) ³/2

A: solution is given below,

Q: Write the sum without sigma notation and evaluate it. 3 π 25) Σ 4 sin k k=1

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Q: Evaluate each of the following integrals 1. S dx x√√x²+4

A: Please see the below picture for detailed solution.

Q: What is an example of Leibnitz notation that's used to indicate rates of change? (See Strategy for…

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Q: Find the slope of the tangent line to the function f(x) = X² x + 3 at the point (1, 1).

A: Recall: Slope of the tangent line to the function f(x) is, m=f'(x) at given point.

Q: r(t) = 300 + 800t - 90t²,

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Q: Hello, Please show all your and solve the following the

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Q: Find F'(x) given that F(x) = Provide your answer below: K 4x 5 In 1² dt. (Do not include "F'(x) ="…

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Q: Sketch the graph of the ellipse: x² = 4 - 2y². Label the vertices and foci on the graph.

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Q: Evaluate the indefinite integrals using Substitution. (use C for the constant of integration.) a)…

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Q: If the length L of a fishing rod is shrinking by 1 foot per minute at the moment the rod is 30 feet…

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Q: Explain all the reasons why the integral the integral as an appropriate set of limits. dr x√x² 9 is…

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Q: Convert the polar point (-3,3π/2) to rectangular coordinates.

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Q: α. C Bl b = 6 a. Triangle above. IF C= √61, 6=6 Find a, d and B.

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Q: 4- Find the volume of the solid obtained by rotating about the x-axis the region under the curve y =…

A: To find volume of solid.

Q: 1 9. f(x) = 2x = 1 11. f(x) 1 XM

A: Given query is to find the area under the curve

Q: fferentiate the function and find the slope of the tangent line at the given value of the…

A: Given query is to find the slope of the tangent.

Q: 5 4 3 2 1 -1 -2 -3 -4 + + Find lim = tan x is The graph of the function f(x) given above for the…

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Q: 2013, the average surface temperature of the earth was 58 degrees Fahrenheit.  According to one…

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Q: For the following expression, find the correct partial fraction decomposition. -3x² 10x 38 (3x − 1)…

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Q: S x² dx 3 (4-x²)2

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Q: The value of 5 1 x² [³ - dx is

A: Given query is to find the value of integral.

Q: dt, then F'(x) = 0 a) If F(x) = √5 / / di 20 3 b) If F(x) = ² = dt, then F'(x) = c) If F(x) = √²/1/1…

A: Given:   a) Fx=∫20x1tdt      we use common integral ∫1tdt=lnt          =lnt20x          Fx=lnx-ln20…

Q: 7 5 ·TT²² Find x + y dydx.

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Q: Thanks

A: We have to find the value of the given following conditions according to the given information

Q: 4- Find the volume of the solid obtained by rotating about the x-axis the region under the curve…

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Q: 3- a) Find the area of the region in the first quadrant between, y || = and y = x² b) Find the…

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Q: For the equation given below, evaluate y' at the point (2, –1). y'at (2, -1) = e³ + 10 − e¯¹ = 2x² +…

A: To find derivative of the given function.

Q: 2 13x Consider the function f(x) = x²e¹³ For this function there are three important open intervals:…

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Q: Evaluate. (Be sure to check by differentiating!) (In x) 15 X (Inx)15 dx, x>0 f(in; dx = X (Type an…

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Q: Evaluate the limit using L'Hôpital's rule 7x³ e10x lim x →∞

A: Given query is to find the limit.

Q: ・S 21³/2 50. 2:³/2 In x da a

A: Solve the following

Q: ate the integral. Prox f(x) dx where f(x) = 2 if -2 ≤ x ≤ 0 {²₁ - x² 14-x² if 0<x≤2

A: Given is to find the integral

Q: Find the following antiderivatives: 2 In²(x²) √= 1.) x + x ln(x²) dx

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Q: Using the derivative of f(x) given below, determine the critical points of f(x). 19) f'(x) = (x -…

A: The given data is: f'x=x-22x+9 To determine the critical points of fx

Q: Use polynomial fitting to find the formula for the nth term of the sequence (an)nzo which starts,…

A: The sequence is  0, 8, 20, 36, 56, 80, . . .

Q: Suppose the daily supply equation for noise cancelling wireless headphones is given by P = S(x) = 60…

A: NOTE: Refresh your page if you can't see any equations. . the given supply function is  and the…

Q: Find the exact length of the polar curve r = = 2cos 0, 0≤ 0 ≤ π.

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Q: Evaluate the integral. [² v³ + 3v³ dv 3V6 V4

A: Evaluate the integral  ∫12v3+3v6v4dv

Q: 2√2 X 1 ²³ t³ √²-4 dt

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Q: The angle addition formula for sine is sin(a ± ß) = sin a cos ß ± cos a sin ß. Use this formula to…

A: We have to solve given Questions.

Q: ". Is (sin x+cos x)² = sin² x + cos²x an identity? (a) True (b) False

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