Find the average value over the given interval. f(x)=x²+x-7; [0,14] The average value of f(x) = x² + x - 7 on [0,14] is. (Type an integer or a simplified fraction.) ...

Q: an integral corresponding to the area of the region bounded by the curves of the functions f and g…

A: f(x) =x2 -4x  g(x) = -x2 here area function = f(x) - g(x) = x2 -4x  -(-x2 ) = 2x2 - 4x

Q: foxdx

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Q: Transform the given system of differential equations into an equivalent system of first-order…

A: Given

Q: Problems: Solve the following differential equations: 3- (2x+y)dx+(x-2y)dy=0

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Evaluate the given integral by changing to polar coordinates. Sk (4x - y) dA, where R is the region…

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Q: ۔ ۔ میرا میرے = 3 422 + 81(1 + 2 )2 dy .dz

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Q: Graph the parabola y=(x^2-100x)/50

A: Graph the parabola y=(x^2-100x)/50

Q: If integration using u-substitution technique is used to solve for ∫2e2x1−e4x dx/square root of…

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Q: Compute each of the following limits. (a) (i) lim 7x²5 x→-1 x²-25 (ii) lim X-5 x+5 (iii) lim x+2 x-2…

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Q: Use Lagrange multipliers to find the absolute maximum and minimum values of the function z = f(x, y)…

A: Given problem:- Use Lagrange multipliers to find the absolute maximum and minimum values of the…

Q: 3. (3y² + xcos xy) + (3x² + ycos xy) = 0 dx a) y + sen xy + x³ = 0 y² + sen xy + x³ = 0 y² + sen y +…

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Q: Consider the function f(x) = (3x² − 4)(x² + 6). (a) Compute the derivative of f(x) by multiplying…

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Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

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Q: (0²-16)³/2 de A3

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Q: Solve the given differential equations: dy x-3 1. dx 2+y²

A: Differential equations

Q: = [ (23a)" e1¹0z da, Consider the integral n is a natural number greater than 1, When applying…

A: Given problem:- J = ∫ (23x)n e10x dx

Q: Find the limit by interpreting the expression as an appropriate derivative. e2x 1 lim- = i x→0 X

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Q: D Question 15 Find the value of b such that the function f(x) is continuous everywhere. x² + a if x…

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Q: A trough 21m long has ends shaped like isosceles triangles, with base 5m and height 14m. Water is…

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: Topic = Derivative

Q: Find the integrating factor e∫Pdx then find the general solution. 2x(y - x2)dx + dy = 0

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Q: If y = ecos(x) then y" + sin(x) y' +cos(x) =

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Q: 1. Find when y = In (-²). dx Express your answer in a single fraction.

A: The given function,     y=lnx5-2x

Q: 5- x(in y-In x)dy = y(1 + In y-In x)dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: B2. Find the integrating factor by inspection then solve.  y(y2 + 1)dx + x(y2 - 1)dy = 0

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Q: Solve the triangle ABC if b = 127, c = 163, ZB = 40°. a = ZA = degrees; ZC = degrees; Assume ZA is…

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Q: 3) Find equations for the lines: a 21 g. The line through (0.-7,0) perpendicular to the plane…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Using the polya's four step problem, how many square are in the figure?

A: Concept: Polya's four-step problem solving: (1). Recognize the issue.Sometimes the issue isn't so…

Q: When does f(x) = ln(x + sin2x), 0 < x < 2π have a local minimum?

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Q: Find the general solution of the given differential equation. y’’+6y’+3y=0 topic: complex roots of…

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Q: -32 1 ย X

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Q: Factor. 7c²-7t² 7c²-7²2² = (Factor completely.)

A: Given expression 7c2 - 7t2

Q: Which of the following is correct in solving 20 2x√2 + x dx? (a) Substitution technique can be used…

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Q: Let f a continuous function in [0,1], an integral equivalent to π/2 f (cos(x)) sen (x) dx 0 after…

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Q: Given x³ + xy - 4x = 4: dy (a) Find by differentiating implicitly. Do not substitute for y. dx dy dx…

A: Explanation of the answer is as follows

Q: The population of a small country by year is shown in the table below. Year 1955 1960 Population…

A: If population of a city x in 1950 and y in 1960 then absolute change of population=(y-x)  As per our…

Q: derivative. (a) lim (b) lim Ax→0 In(e¹ + Ax) - 4 Ax In w w 1 w 1 =

A: Using L hospital rule

Q: When i put it into my online math assiment it says its wrong

A: As we know that  Amount after t years on investing a principal value P at a rate of interest of R…

Q: Evaluate the iterated integral by converting to polar coordinates. 2 *√2x - x² 6²6² 4√ x² + y² dy dx…

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Q: Given `f(x)=1/(x-2)` and `g(x) = 4/(x-3)`, find the domain of `f(g(x))` Domain:

A: Given.

Q: Q2] (A) Find the general solution to ONLY ONE of the following differential Mations (1) (sec(y))2…

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Q: (a) 4 * -61 (i) Identify the critical numbers of f. (Enter your answers as a comma-separated list.)…

A: (i)  Critical number: f'(x)=0 when x=2 (ii) interval split: -∞,2,2,∞ f'(x)&lt;0 when x∈(-∞,2)…

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 &amp; x=2rcos θ , y=2rsin θ

Q: Use the table of integrals to evaluate the integral. 2 [²³15x³√4x² 15x³ 4x²x4 dx

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Q: Which of the following gives the area of the region bounded below by y = sin(x), above by y =…

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Q: When applying trigonometric substitution in the integral: x5 J S -dx √4x² J is equivalent to: O a) […

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Q: 4) Find equations for the planes: b. The plane through (1,-1,3) parallel to the plane 3x+y+z=7 A-3+1

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Q: Solve the given differential equations: 1. dy x3 dx 2+y²

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: D Question 3 Let P = f(t) be the population of the United States, in millions, t years after January…

A: We have to explain each mathematical statement into practice meaning.