Find the differential equation having each equation as general solution. m y ==-7

Q: 1- Find the area under one arch of y = cos3 x

A: To find the area under the arch we will integrate the given function under the limits of the given…

Q: Consider the function: Step 1 of 2: Findf"(x). f(x) = = 2x + 7 5x - 10

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Q: How does our unders Calculu

A: answer is in next step

Q: Find an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: 2. Geometric series a. Consider the function defined by the geometric series f (x) = other words,…

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: Given that [²x²x 1/3 dx = Need Help? Read It use this fact and the properties of definite integrals…

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 9, S(0) =…

A: In this question we have to find the value of s(t).

Q: Consider the function on the interval (0, 27). F(x) = 1/2* + cos x (a) Find the open intervals on…

A: The given function f(x)=12+cos x on the interval 0, 2π

Q: Consider the following function. 13 f(x) = - In x 13 (a) Find the critical numbers of f. (Enter your…

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Q: Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval.…

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Q: Ordinary differential equation dx/dy = ( x-e-x )/( y+ey )

A: We can solve as follows

Q: Find the indefinite integral. (Use c for the constant of integration.) [₁4 (4t³i + 14tj - 6√tk) dt

A: Here we have to use the concept of the indefinite integration.

Q: = Set up the definite integral required to find the area of the region between the graph of y y = 2x…

A: To find the area..

Q: 3 Consider the linear system system x +2y = 10 3x + = 30 i) Determine >lat value of t, so that the…

A: Given a system of equations.

Q: Find the indefinite integral. (Use c for the constant of integration.) [(41³i+ (4t³i + 14tj - 6√tk)…

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Q: The following rational equation has denominators that contain variables. For this equation, a. Write…

A: Given problem:-

Q: Evaluate F. dr along the curve C if F(x, y) = (x² + y²)¯³ (xi+yj), с and C: r(t) = et sin ti + et…

A: F.dr is integrated along the curve C.

Q: Remaining "How Did I Do?" Uses: 0/1 Use the fact that: loga (x) = -1.6, loga (y) = 4.2, and loga (2)…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: To find the domain of a vector-valued function  r(t) = a(t) i + b(t) j + c(t) k, we will need to…

Q: 49-50 Find az/ax and əz/ay. 49. (a) z = f(x) + g(y) 50. (a) z = f(x) g(y) (c) z = f(x/y) (b) z = f(x…

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Q: 63. Maximum Area A rancher has 400 feet of fencing with which to enclose two adjacent rectangular…

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Q: Finding the Area of a Region In Exercises 5-14, sketch the region bounded by the graphs of the…

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Q: Applying the First Derivative Test In Exercises 29-36, (a) find the critical numbers of the function…

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Q: Question 15 The cost, in dollars, to produce a designer dog leashes is C(z) - 8x +9, and the…

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Q: Blologist is monitoring the population of a rare species of Jackelope. The initial population size…

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Q: alyze and sketch a graph of the function. Label any intercepts, relative extrema, y = x² - 8x + 37…

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Q: A particle moves according to the law of motion s = t³ - 7t², t> 0, where t is measured in seconds…

A: In multiple parts question we are advised to answer only first three sub parts .

Q: Determine the average cost function C(x)= C(x)=x²+2x²-3x+40 Determine the average cost function.…

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Q: 1. Let Evaluate the following limit. 7 (t) = (t² + 5, t²-5t+6 t²-9 lim r(t). t-3 > sin(πt)).

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Q: c) The equation of a curve is y = √5x+4 i. Calculate the gradient of the curve at the point where x…

A: Gradient: The gradient is a synonym for "slope." The steeper the line is at the place the higher is…

Q: Given: y = cosh (es): Find y O (E) None of these cosh (e*²) 2:z sinh(e*) Oeu sinh(ex) O 2ae*…

A: This question is related to differentiation, We will solve it using given information .

Q: 2) Find the area of the function f(x)=x² +4 for x=-1 tox=4.

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Q: 4) A company purchases a new machine for which the rate of depreciation is dv maner 10,000(t-6),0 ≤…

A: Given query is to find the total loass of the value in first 3 years.

Q: Write the given (total) area as an integral. * The area above the x-axis and below y = 4 - x^2 *…

A: 1)  consider y=4-x2  and y=0    Solve the above two equations   4-x2=0   4-x2=0   x2=4   x=±2Area…

Q: 1. Use calculus to find the exact absolute maximum and minimum values of f(x) = (x² + 2x - 3)2 on…

A: We have to find the solution

Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 34…

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Q: Using the Mean Value Theorem In Exercises 13-18, determine whether the Mean Value Theorem can be…

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Q: Find the work done by the three-dimensional inverse-square field 1 F(r) = r on a particle that moves…

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Q: F. dr if Using any method, find the value of So F(x, y) = (6e + 3ye") i + (3eª + 6xe²) j and πt C:…

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Q: COSX Let esinx = Soos* f (t) dt and f determine the value of (1/2) f(t) dut and f is a continous…

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Q: Finding Extrema on a Closed Interval In Exercises 1-8, find the absolute extrema of the function on…

A: To find the absolute extrema of the function on the closed interval. By using a graphing utility to…

Q: Finding an Indefinite Integral In Exercises 1-6, find the indefinite integral. 6. ·S(10² + x³/2) dx

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Q: Determine whether the sequence converges or diverges. If it converges, compute the limit.    an =…

A: Use ratio test

Q: A vector u has an initial point (1,2,3) and terminal point (6,9,1). Find a vector v that has the…

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Q: Find the length and width (in feet) of a rectangle that has the given area and a minimum perimeter.…

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Q: The differential equation regarding the family of curve y = e 500x 1S

A: This question is based on diffrential equation.

Q: 03) Prove or disprove that y = ce* + de ²x is the solution to y(2) + y(¹) - 2y = 0.

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Q: b Write the following expression as a single definite integral of the form f(x) dx. [²Rx) dx =…

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Q: Let C be the curve represented by the equations x = 3t, y = t², (0 ≤ t ≤ 1). In each part, evaluate…

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Q: Use the properties of logarithms to expand the expression as a sum, difference, and/or constant…

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