Problem 1: Obtain ODE by eliminating arbitrary constant A, B, and C y = A e2x + Be + C

Q: bus For the function f(x) given below, evaluate lim f(x) and lim f(x). 818 8118 f(x) = √3x²-1 7x+3…

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Q: Two poles are connected by a wire that is also connected to the ground between the poles. The first…

A: Given:

Q: Consider the vectors. (5, -8), (-4,1) (a) Find the dot product of the two vectors. -28 (b) Find the…

A: Given problem:- Consider the vectors.   <5, -8>, <-4,1>   (a) Find the dot product of…

Q: 4) A degree 3 polynomial function, P(x) has zeros x 2, x = 1, x = m and a leading coefficient of 1.…

A: Here, the polynomial P(x) is of degree 3 and has three zeros x=2,1 & m and the leading…

Q: Select the representations that do not change the location of the point a. [-2.-357) D. (-2,-²5) b.…

A: -2, 7π5=-2cos7π5, -2sin7π5π+2π5=7π5=2 cos2π5, 2cos2π5  [FIRST Quadrant]A)-2 cos3π5,…

Q: Let F = Vf and f = 2zy + 8xy + 6xz. Calculate F. dr for the path r₁ = (t,t,t), 0 ≤ t ≤ 1. (Give your…

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Q: Determine whether the series converges or diverges. n² Σ (n + 2)! n=1

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Q: At what points c does the conclusion of the Mean Value Theorem hold for f(x) = x³ on the interval…

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Q: 6. [ID # ending in 9] J3 w Find дх ду дz if w — exyz = 0.

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Q: Find the curvature of the curve r(t) = (3 cos (4t), 3 sin(4t), 4t) at the point t = 0 Give your…

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Q: Given the relation x³z² + sin(3z - 2y) - 8√9+7x³ + 5y + 13 = 0 implicitly defines y as a…

A: Differentiate

Q: Find the Taylor series generated by fat x = a. 1 f(x)=, a=9

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Q: n 9 = k=1 Note: Your answer should be in terms of n.

A: Solve the given

Q: If f(x)=3+3x−5x^2 find f′ (-3).

A: Solution: f(x)=3+3x−5x2

Q: The temperature in degrees Celsius (C) in Toronto starting on March 1** can be represented by the…

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Q: 3. Evaluate yn x dx

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Q: Use an appropriate linear approximation to estimate cos(60.5" (Round your answer to three decimal…

A: To use the linear approximation to estimate cos(60.5°)

Q: A triangle has sides represented by the vectors (2, 1) and (3, 4). Determine the length of the third…

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Q: Find the derivative of the vector function r(t) = (tsin t, t^2 , t cost)

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Q: analyze and trace the given curve y = 2x3 + 3x2 - 12x + 7

A: Given:

Q: In 2000, the population of a city was 76,000. The population had grown to 111,000 by 2011. If the…

A: We have to find the year.

Q: Solve the system. Give your answer as (a, y, z) 3z - y + z = 7 -2x + 2y + 3z = – 18 3z-6y + 6z = 0…

A: Use the method of elimination and find the value of x, y and z.

Q: Solve the differential equation 2xy + y²) dx + (x² + 2xy-y²) dy = 0

A: A homogeneous differential equation is one in which the degree of the function f(x,y) is the same as…

Q: Let f(x, y) = 6x cos (y). Find the conservative vector field F, which is the gradient of f. (Give…

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Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: A rectangle is constructed with its base on the diameter of a semicircle with radius 27 and with its…

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Q: y= v-2² +2²-2x+ 8 (a) Find y'= f'(x). f'(x)=x²+x-2 (b) Find the critical values. (Enter your answers…

A: Solve it

Q: Find the eccentricity of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. 2 1/2 2√7

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Q: Let C be the parametric curve defined by x(t) = t² – t – 2, %3D |y(t) = t3 . 1 t² +t. 2 - (-2) 3…

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Q: Using the data in the table, approximate g′(3). Using correct units, interpret the meaning of g′(3)…

A: Consider a function y =f(x) .Then f '(x) is the rate of change of y with respect to x.

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 3 1 = lim t+oo 8t² +9' 5t, (?, ?)

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Q: A. Using chain rule find the derivative of the following functions. 1) f(x) = (x³ + 3x²) 200 2) f(x)…

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Q: Value Theorem. Provide your answer below: C= ntent attribution Previous MacBook Pro G Search or type…

A: The given function is;  f(x)=8x2-8x on the interval [0,1].

Q: f(x) = -x² + +9 square units

A: Given the query is to the area bounded by the curve.

Q: 6. During the worst 4-hr period of a hurricane the wind velocity in miles per hour is given by v =…

A: The average value of the function is given by;0≤t≤4v(t)=1b-a ∫abv(t) dt     =14 ∫04(5t-t2+100) dt

Q: Find the point of diminishing returns for the function, where R is the revenue (in thousands of…

A: Given the query is to find the point of diminishing returns.

Q: Which of the following is a polynomial function?

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Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t = 1|3

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Q: 6. The graph off consists of line segments and a semicircle, as shown in the figure. Evaluate each…

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Q: construction company will be panalized each day of delay in construction for bridge. The penalty…

A: Given the query is to find the maximum possivle days for delaying.

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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Q: A street light is at the top of a pole that has a height of 15 ft. A woman 5 ft tall walks away from…

A: Consider a function y = f(x) .Then f '(x) is the rate of change of y with respect to x.

Q: x²+2x+1 dx (x+2)(x−1)²

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Q: Find the area of the region enclosed by the inner loop of the curve. r = 2 + 4 sin ?

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Q: Use a parametri. tion to express the area of tne surface as a double Integrai. Then The portion of…

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Q: Numerical solution of Ordinary differential equations Consider the following initial value problem…

A: This is a problem of numerical method . Based on modified Euler method we will answer the question.

Q: Use Newton's method to approximate a root of the equation z + c + 3 - 0 as follows. Let I, = -1 be…

A: Let's find.

Q: If A =27+7-, B =-T+27-4k, and A +B +C =27+7+ 2k, what is C? 7.

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Q: +² = x² dx

A: We have to solve the given differential equation

Q: 42. If g(0) = 0 sin 0, find g"(π/6).

A: Solve the given