Find the area of the region bounded by the parabola y^2=x+3 and the line x - y = -1

Q: -. Let R be the region bounded by the graphs of the equations y = ln x, y=0 for 1≤x≤e. Set up…

A: A detailed solution is given below.

Q: If In a = 2, ln b = 3, and ln c = 5, evaluate the following: a² b²c4 (a) In = (b) In √a²b²c4 =

A: To evaluate the given expression.

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(5,…

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Q: Find the general indefinite integral. (Use C for the constant of integration. Remember to use…

A: simplify the expression and solve the integral

Q: Determine whether the given set of functions is linearly independent on the interval (-∞0,00). f₁(x)…

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Q: *T/2 10 cos(0) r dr de

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: A function f is said to have a removable discontinuity at a if: 1. f is either not defined or not…

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Q: Write an equation for the function graphed below -7 6 5 4 -3 -2 y= 50 on it'st 72 3 Q

A: Topic = Functions

Q: Sketch the region R whose area is given by the iterated integral. 8 8-x [*ª [* dy dx + £® ® - * 8 y…

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Q: ¡ (ew - 3) dw? O ew - 3w+C O - ew + 3W + C O -ew - 3W + C O ew - 3+ C

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Q: Find the real roots of the equation B 244

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Q: For the function f(x,y,z) = x rr fy 11 he e = 11 f₂ = N fyz 10 8z+1 -9 8z+1 (9y-10x)8 (8z+1)² 11 72…

A: The given function is;  f(x,y,z)=(10x-9y) /(8z+1).

Q: Find all values of x and y such that Px(x,y) = 0 and P Py(x,y)=0 simultaneously. P(x,y) = 5x² -…

A: Topic = Algebra

Q: In the integral of x cos 2x dx with limits form 0 to pi/2, what is the indefinite integral? Select…

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Q: e) Find the linear approximation of the function f(x, y, z) = x³y² + z² at the point (2, 3, 4) and…

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Q: write on paper for upvote please. Provide Exact

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Q: Find the general solution of the given second-order differential equation. 2y" - 5y' + 6y = 0 y(x) =

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Q: Sketch the region R whose area is given by the iterated integral. To Se *6 *3 7- 6- 5- 4- 3- نيا 2-…

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Q: 2. Given the function f(x, y)=3x²y + 2xy-y, a) find the value of the directional derivative of the…

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Q: need the answer quickly

A: simplification

Q: For the function, do the following. f(x) = 1/x from a = 1 to b = 4. (a) Approximate the…

A: The function fx=1x from a=1 to b=4

Q: Explain why x ≤- 2, 0 ≤ x ≤ 5 could not be the solution to (x-5)(x+2) ≤ 0.

A: This question is based on solution of inequality.

Q: Use vectors to find the fourth vertex of a parallelogram, three of whose vertices are (0, 0), (1,…

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Q: Let g(x) = x¹/3√1-2x. Select all of the following values of x in the domain of g where g is not…

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Q: 23. Express each of the following as a logarithm. Use a calculator to evaluate your answer correct…

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Q: 2) y" - y' — 6y = 0. бу

A: Follow the procedure given below.

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = P(1, 4, 8),…

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Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = 2 x-intercepts…

A: We need to write an equation for a rational function with : Vertical asymptotes at x=-4 and x=2…

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

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Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

A: Solution: Given: 2x - 5z =5 .............(1) 2x - 5z =6 .............(2) On solving both equations…

Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: Given that the graph of f(x) passes through the point (4, 2) and that the slope of its tangent line…

A: Recall: The slope of the tangent line to the curve f(x) is f'(x).

Q: Find the domain and the range of the function. (Enter your answers using Interval notation.)…

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Q: 3) y" + 4y' + 4y = 0.

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Q: Solve the given differential equation by undetermined coefficients. y" - y² + ²y = 2 + ex/2 y(x) =

A: The characteristic equation is            m2-m+14=0⇒4m2-4m+1=0⇒m=--4±02· 4⇒m=12,12 Now, the general…

Q: Find f(x) if f" (x) = 2, f(0) = 1 and f(1) = 0.

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Q: improper iterat 1/x3 y dy dx

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Q: Find the gradient of the function at the given point. w = x tan(y + 2), (19, 9, -2) Vw(19, 9, -2) =…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Determine any planes that are parallel or identical. (Select all that apply.) P₁: -90x + 60y + 90z =…

A: Let us know thatWe are aware of the parallel nature of the two lines with direction ratios A1, B1,…

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = (1, 5, 5)

A: Follow the procedure given below.

Q: Please

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Q: Sketch the region R whose area is given by the iterated integral. L1²5-1² dx dy

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Q: Replacement Time An outboard motor has an initial price of $2,160. A service contract costs $400 for…

A: Topic:- application of derivatives

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: Determine csc(x) + cot (x) if tan x + sec(x) = 22/7. 27/12; 29/15; 24/18; 23/11

A: We can answer the question by finding the correct option as below.

Q: Зу" +y=0.

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Q: For k(x) = (x + 1)(2x)(-3x²+2x+3), find the derivative of k(x) at the point x = 0 using the product…

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