1. Consider the ODE: (2x + 4y) + (4x − 2y + 1)y' = 0. Verify that the ODE is exact and then find its solution.

Q: Solve for the indicated value, and graph the situation showing the solution point. The formula for…

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Q: 3. lim tan x x→2/2

A: Topic- Limits  3.)limx→π2tan x   exists only if limx→π2-tan x=limx→π2+tan x if limx→π2-tan…

Q: Let f(x, y) = x² - y² y-1 Sketch the domain of f on the xy-plane.

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Q: >) Find the length of the curve x== ² + y²² from y=1 to y = 4.

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Q: Find the solution of the given initial value problem. ty + (t+1)y= 10t, y(In 2) = 10, t> 0A 1 2 The…

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Q: Fill in the missing values to make the equations true. (a) log, 7-log, 10 = (b) log₂ + log, 8 = (c)…

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Q: lim x csc 3x x-0

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Q: Let T be an onto linear transformation from IR" to Rs. 1. What can one say about the relationship…

A: We have given that  T is an onto linear transformation from  Rr to Rs .

Q: Problem 2: Using index notation, demonstrate mathematically the following equations: 1- uxv=-vxu 2-…

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Q: 1. Use the graph of f(x) to find each of the following. a. lim f(x) = x-0 b. lim f(x): X→4- C. lim_…

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Q: 4ª8a 32b = 32 for x = =

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Q: Suppose an equation of the tangent line to the curve y = f(x) at the point where a = 3 is y = 4x -…

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Q: At time t = 14 s, the velocity of a particle moving in the x-y plane is v = 0.06i + 2.21j m/s. By…

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Q: Consider the position function s(t)= -16t2 + 80t representing the position of an object moving…

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Q: Calculate the cross product assuming uxw = (-3,5,-2) (Use symbolic notation or fractions where…

A: a) Given u×w=-3,5,-2Therefore(5u+7w)×w=5u×w+7w×wBut…

Q: 1. Using differentials, solve for the approximate change in the hypotenuse of a right triangle if…

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Q: where did -a+h come from

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Q: 1. Use the limit formula, and showing all work, find f'(x) for f(x) = -3x³ + 2x -1.

A: To find the differentiation of given function.

Q: 1) Suppose that f(x) = sin x . Find ƒ' (). Choose the best answer. O 0.5 O sqrt(3)/2 0 0 does not…

A: Given function, f(x)=sin(x).

Q: Find the scalar equation for the plane through the points (3, 0, 1), (3, 1, 3), and (1, 0, 1).

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Q: Set up the definite integral required to find the area of the region between the graph of y=x²-15…

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Q: Directions: Find the derivatives using the definition of limits (4-step Rule). Show each step from…

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Q: Given the differential equation (4x2+y2)dx + x(x-2y)dy = 0  1. Verify that M(x,y) = (4x2 + y2) and…

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Q: e^x cos y dx - e^x siny dy = 0 is an exact DE, please solve its general solution with complete…

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Q: 9. y(cos³x) (cos²2y)

A: We are asked to find the solution of the differential equation

Q: The function f(x) = √√2x − x² is given graphed below: (A) Starting with the formula for f(x), find a…

A: We can solve this as follows:

Q: MAKE AN EXPLANATION FOR THIS

A: For a differential equation dydx=fx,y, the dependent variable is yand the independent variable is x.

Q: Suppose that the function fis defined, for all real numbers, as follows. f(x)=- 3 1 x-2 if x # -2…

A: The given function is f(x)=-14x-2if x≠-23if x=-2 We have to find the value f(-5),f(-2) and f(4) .

Q: (a) Find the average rate of change of y = 3x² with respect to x over the interval [0, 2]. rave =…

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Q: Use the graph of f to find the largest open interval on which fis increasing, and the largest open…

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Q: f(x) is the equation of a line with slope 5 that goes through the point (2,3), what is f(0) ?

A: We have given  Slope of the line = 5 Let,  fx=mx+b Put m = 5 fx=5x+b ............(i) This line is…

Q: Given the differential equation 4x²+ y² dx+x\x-2y dy=0 2. Solve the given DE with homogeneous…

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Q: Consider the function y = f(x) = x² + 15x + 56 and the x-value xo 5 (a) Find a formula for the slope…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: an = lim an n→+∞ The sequence diverges

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Q: 15. Find f(x) using the limit definition of the derivative. f(x)=√2-x In the answer box, enter the…

A: We have to find derivative

Q: Determine the work done by the constant force. The locomotive of a freight train pulls its cars with…

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Q: If f(a, b) = eab (ab + a), show that fûû(a, b) — àƒÂ(a,b) = a²eab

A: We can solve this as follows:

Q: Question 6 Suppose the region between the graph of y = The graphs intersect at a Doint(s)) x 7 and y…

A: The region between the graph of y=x-7 and y=14(x-7) is resolved around the x-axis  We have to find…

Q: 5 If f(x) = 3 + + X Find f'(5). 5 x2, find f'(x).

A: If f(x)= 3+5/x +5/x2  Find f'(x) and f'(5).

Q: $ 3 months $

A: We will find the required.

Q: x) = ln(4x): c=1/4 Give the summation notation of the taylor series of this function.

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Q: Solve for x in terms of a, b, c in the following equation In(ax + b)- In (cx + 1) +e³=5

A: The given equation: lnax+b-lncx+1+e3=5.We need to solve the above equation.

Q: 11. g(x) = X, x-1, x < 0 x ≥0

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Q: Evaluate the integral. .2π x x sin(x) cos(x) dx

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Q: Find an integrating factor for each of the following equations and solve these equations. 1) (x² +…

A: A detailed solution is given below.

Q: a and b are two points in the third-dimenson. Show the equation that describes the set of points…

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Q: Which of the following functions is a solution of (x² +1)y' + y² + 1 = 0 ?

A: We have to solve the differential equation.

Q: A machinist is required to manufacture a circular metal disk with area 2300 cm². (a) What radius…

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Q: If f'(x)= tan-¹(x3 - x), at how many points is the tangent line to the graph of y = f(x) parallel to…

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