The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve at x = 0. What are the values of a, b, and c?

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A: We can solve the given initial differential equation .

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Q: Find for the following equation by Implicit Partial Differentiation; дz x³ + y²z4 + 3xyz = 5

A: Implicit partial differentiation

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A: Solved below.

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A: follow next step

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A: The number of bacteria in a refrigerated food product is given by N(T) = 23T2-96T+12,  5&lt;T&lt;35…

Q: 3- اول ** X 2 Sin² Lys y

A: Follow the procedure given below.

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A: Here we have to choose the correct option.

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Q: Determine whether the series Σn=1 3n+¹ ln(n+1) is convergent or divergent.

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A: The objective is to find total distance travelled.

Q: We wish to find the solution to =26y that passes through the point (x, y) = (1, 3).

A: Explained below

Q: ** asin I sin²Lys y X IT 3- 2 จา

A: Use change of order of integration.

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A: given c is a constant

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Q: Find a particular solution of the indicated linear system that satisfies the initial conditions x₁…

A: Please see the below picture for detailed solution.

Q: Let f(x) = 2x² - 4x and g(x) = -3x - 1. Find f[g(-4)]. f[g(-4)] =

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Q: dx 10) √x²4(14+x²) a) - - - c) - 1 4X ㅗ 4x + 1 andan ²/3 + c autan 1/2/3 + c 8 I ondan 2/2 + c 8 j 8

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Q: What is f 5√xdx? 3 f 5√√xdx = 5x² + C 2 3 f5√xdx = 10x² + C 3 f5√xdx = 5x² + C 3 [ 5vxdx= 5x? +C

A: Let's solve given integral.

Q: c) S xaccainxdx a) = (2x²-1) arcain x + ¥√√√²-x² + C b) 42 (2x² +₁) ancais x + x²√√1-x² + c c) 4…

A: The objective is to find the integration.

Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² + x)))

A: The given limit is limx→0-xlnsin4x2+x. We have to solve the limit using L'Hpotial's rule.

Q: 4 Determine the radius of convergence for the series n=1 2-4-6-(2n) 2-5-8--(3n - (17) ³².2²

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Q: Given the piecewise function f(x) = = Why is f not differentiable at x = 4? Of has no tangent line…

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Q: Sylvia had planned a shopping trip to the United States so she bought US$500 from a bank when the…

A: Concept: Sylvia has US$500 First, the exchange rate was US$0.7834 for C$1 Then the exchange rate…

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A: I am attaching image so that you understand each and every step.

Q: What is the equation of the tangent line to the curve y=x^ +2x −x+8 where x = 1? y = 7x - 3 y = 7x…

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Q: Solve the following initial value problem using Laplace transforms. y"+2y'-3y=3e¹, y(0) = 0,…

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Q: How many asymptotes (both vertical and horizontal) does the following function have: sin(x) -?…

A: To determine the number of asymptotes for the given function.

Q: 3) √ √6x-x² dx a) 12 (x-3) √ 6x-x² + 2 arcain 2/ arcain X=² X-3 te 3 (x+3) Gx-x2+gain x3tc 3 c) —…

A: solution

Q: 3 7 Scot³x c₂c²³x dx - esc X

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Q: Solve the following initial value problem using Laplace transform d'y dy dt -2y = 6e³t; dt² y (0) =…

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Q: Gym A Gym B Total Monthly Cost vs. Number of Visits C Number of Visits Total Monthly Cost 10 55 70-…

A: Linear cost

Q: 41- - ST x² coscyldy dz dx

A: ∫ cos(y) dy= sin(y)+C

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Q: Given a function f(w, x, y, z) = 2(w + 1)² x − xe²+, which of the following is not part of the total…

A: Given a function fw, x, y, z=2w+12x-xez+y2zw, to determine which of the following is not part of the…

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Q: 26 Functions f(a) and g(x) and their first and second derivatives evaluated at z = 1 are listed as…

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Q: Solve the following initial value problem using Laplace transforms. y"-9y=3e¹; y(0) = 0, y'(0)=1

A: Explanation of the answer is as follows

Q: A. Find the volume generated by rotating the region bounded by y=x, y=1 and the y-axis rotated about…

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Q: Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1.

A: The function f(x) is given by, f(x)=ln(3-2x) Differentiating the function successively upto n…