(4) y' + (x + 1)y = ex²y3

Q: 1. Consider the ellipse given by x(t) = 9 cost and y(t) = 81 sint for 0 ≤ t ≤ 2π (a) Make a sketch…

A: The given equation of  eillipse is for

Q: 1. Consider the second-order homogeneous linear differential equation, y"+p(x)y'+q(x)y=0 (a) Let y,…

A:

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: An area to fence is of 37.5 million square feet in a rectangular field.

Q: Find the volume of the solid bounded by the elliptic paraboloid z = 3 + 3x² + 2y², the planes x = 2…

A: Equation of elliptic parabolid z=3+3x2+2y2Equation of planes x=2 and y=4

Q: Consider the function f(x) = x¹ — 32x² +6, −3≤ x ≤ 9. This function has an absolute minimum value…

A:

Q: purchases a new car for $21,550. He makes a $6000 down payment and finances the remainder thro tized…

A: We have to find the monthly payment, amount and interest.

Q: Let h(v) = 4v v² +6

A: h(v)=4vv2+6

Q: Find the local minimum of the function f(x), which is given in the graph below. -6 -5 + -3 -2 5 3 2…

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Q: Differentiate. g(x) = log 29 (5x-4) g'(x) =

A: To differentiate the following function.

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. }} dy…

A: To find:-

Q: Consider g(x) = -6x³ + 14 - 14x - 16x² Determine the intervals on which g is decreasing. g is…

A: In this question, we will find the interval of increasing and decreasing and local maximum and…

Q: In 2004, an art collector paid $155,328,000 for a particular painting. The same painting sold for…

A:

Q: Sketch the curve. r = 7+ 6 cos(0)

A: r=7+6cos⁡(θ)

Q: Use logarithmic differentiation to find the derivative of the function. y = (tan x)8/x 8 -tan(x) tan…

A:

Q: Given the function f(x) = x²e³x, Use the derivatives to determine the open interval(s) where the…

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Q: Find the slope of the tangent line to the curve at the point (4π, 7π/2). 4 sin(x) + 4 cos (y) - 6…

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Q: Find the derivative of the function g(x) g'(x) = = ex 4 - 3x

A:

Q: lim √xe-x/2 x → 00

A: L=limx→∞xe−x/2

Q: Given f(x) = 21x¹ - 26x³ - 120x² +7x+4 The possible inflection values are x = O Concave Down…

A: In this question, we will find the concave down and up intervals.

Q: Find the critical numbers of g(x)=x√4x, x < 3. If th

A: g(x)=x4−x,

Q: Simplify the rational expression. 9x³ - 36x² + 6x - 24 16 - x²

A: we need to simplify the given rational expression.

Q: y-values 9 8 7 6 5 4 3- 2 1 If f(x)= = g(x) 41 g(x) h(x) f'(3) -- 2/17 3 2 3 x-values then 4 X…

A: The given function is The formula we use to find the derivative of function f(x) is Quotient rule…

Q: Evaluate the indefinite integral. +C 5- 4 sin x Cos x dx

A:

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: The function f(x) = -3√x - 15 +14 x > 15 has an inverse f-¹(x) defined on the domain x < 14. Find…

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Q: e²t-e-2t Let h(t) = Find the e²t+e-2t horizontal asymptote(s) of h(t) if they exist. If h(t) has no…

A:

Q: A rectangle is inscribed in a semicircle of radius r = 16 as shown in the diagram below. 0 X y

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Q: the account. Each year the account earns 4% interest, and you deposit $7000 into the accou This can…

A: Given differential equation

Q: Find the local maximum of the function f(x), which is given in the graph below. As an ordered pair…

A: Find the local maximum of the function f(x), which is given in the graph below. As an ordered pair…

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: For a Function f( x , y ), The directional Deivative in the direction of  is given as

Q: Differentiate. F(x)= F'(x) = e3x 9

A:

Q: Use the sum and difference formulas to prove the following identities: 1. sin(x - 1) = sin x 2.…

A: 1.sin⁡(x−π)=−sin⁡x

Q: Evaluate 7/8 S 0 11√ 1- cos 8x dx либ

A:

Q: Find the midpoint of the line segment with the given endpoints. (2,-2), (8,8) (x, y) = (

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Q: y-values 9 8- 7 6 5- * 3 2 1 If f(x) f'(3) = g(x) 1 g(x) h(x) > 2 3 x-values then 4 y-values 4 3 2 1…

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Q: Find the equation of the line tangent to the graph of y=4e" at x = 3. Tangent Line: y =

A: Given: To find equation of tangent at a given point, we need to find the slope of tangent at a given…

Q: Calculate the derivative of y with respect to x, if x³/² + y-5/2 = 7. dy dx

A: Given equation, .derivative rules:

Q: Use the parametric curve, and given value for the parameter, to answer the following question. Use…

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Q: Write out the form of the partial fraction decomposition of the function appearing in the integral:…

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Q: y′′ − y′ = x The equation has a particular solution of the form y = Ax + B (for some constants A and…

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Q: Verify the following identities: 1. tan y csc y 2. 3. tan x sec x = sec y cos y sin x cot x sec x…

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Q: Find the vertex form of the function. Then find each of the following. (A) Intercepts (B) Vertex (C)…

A: Consider the function

Q: Suppose a product's revenue function is given by R(q) = -2q² + 700q, where R(q) is in dollars and q…

A: Revenue function is given by:Where, is in dollars is the units sold

Q: For the function x f(x) = x-5 find the derivative of the inverse function f-¹ at the point x = 2.…

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Q: Find derivative of the following function. e³x + e-3x dy dx y = || X

A:

Q: 6. Given f(x) = 3x - 1 A. Find (f-g)(x) B. Find (fog)(x) report domain and simplify C. Find (3) (2)…

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Q: Answer the following True or False: p(x) If p(x) and g(x) are polynomials such that p(6) = 0 and…

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Q: If a 4th order linear differential equation is such that the corresponding characteristic equation…

A: If a 4th-order linear differential equation is such that the corresponding characteristic equation…

Q: Use the factor theorem to determine if the given binomial is a factor of f(x). f(x)=x²-2x³ +5x²…

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Q: 2x dy + y(2 + y²x) dx = 0

A: The given differential equation is