ind the equation of the tangent line to the graph of f(x)=(x³ + x)² at x = 1. 2 our equation must be in the form y=mx+b.

Q: Find the equation of the plane passing through the points (1, 0, 1), (−1,1,0) and (3, -3,2). Leave…

A: NOTE: Refresh your page if you can't see any equations. . given points are

Q: Use the Integral Test to determine whether the following series converges after showing that the…

A: The series is given as , ∑k=1∞ke-6k2

Q: Find the critical numbers of the function f(x) using a graph. X = X = X = 12x5 + 15x4 + 40x³ - 9 and…

A: Given that , fx=-12x5+15x4+40x3-9 find the critical points.

Q: Find the area enclosed by the function f(x) = cos x + sen x , the x-axis and y-axis . (note: cos…

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Q: Find a power series representation for the function on (−1, 1). 1. f(x) 2 f(x) x² tan-¹(x) = X 1…

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Q: U.S. Internet advertising revenue grew at the rate of R(t) = 0.82t + 1.14    (0 ≤ t ≤ 4) billion…

A: NOTE: Refresh your page if you can't see any equations. . U.S. Internet advertising revenue grew at…

Q: Show steps and find the exact value of 3x+4 dx . Do not use Table Entries. x² +4 T

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Q: Find the limit of the following sequence or determine that the sequence diverges. {In (n³+3) - In…

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution.…

A: ∫xndx=xn+1n+1+cI=∫2x2x2-4dxd dx(xn)=nxn-1

Q: The system of first order differential equations: has solution: y₁ (t) Y₂(t) = = [y/₁ 13/1/2 = = -23…

A: NOTE: Refresh your page if you can't see any equations. . the given system is  write the matrix A

Q: Architecture A special window has the shape of a rectanglesurmounted by an equilateral triangle. See…

A: We have to find the dimensions of the window.

Q: 9x During the course of an illness, a patient's temperature (in degrees Fahrenheit) x hours after…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: 4 3 2 1 y 1 y = f(x) 2 3 4 -X

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Q: Find the midpoint of the line segment joining the points P1 and P2; P1 = (3, - 4); P2 = (5, 4)

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Q: Consider the parametric equations below. x=?-4, y=b+ (a) Sketch the curve by using the parametric…

A: NOTE: Refresh your page if you can't see any equations. . given equations are

Q: The limit of the sequence {In(7n) - In(9n+8)}_₁ is

A: To find the limit of the given sequence

Q: a) Let A be an invertible matrix. Assume that we have matrices B, C such that AB = AC. Show that B =…

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Q: Find all points on the graph of the function f(x) = 2 sin(x) + sin²(x) at which the tangent line is…

A: We need to find out the points where tangent line is horizontal.

Q: Nutrition   A certain company′s Mixed Cereal for Baby contains, in each serving, 80 calories and 10…

A: This is a linear programming problem. Here, we will first find the system of inequality, then graph…

Q: 7- Minimize the material needed to design a rectangular cubic box of volume 900 cm³. Find the…

A: Let the dimensions of the box be x, y  and z cm

Q: The graph to the right gives the position, s(t), of a biker (in feet) from her starting position…

A: The above graph gives the position, st, of a biker in feet from her starting position after t…

Q: 4.83. Show that dz z²a² 2a In ( ² = a) + ² th-¹2+ a +C₁=-coth a C2.

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Q: Let f(x) = ex²-1. The set f-¹([1, 3)) is: 75.5. O (A) (-√1+log 3, -1] U [1, V1 + log 3) O (B)[-√1+…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  we need to find…

Q: Find all values of t in the interval [0, 2π] that satisfy the given equation. (Enter your answers as…

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Q: Problem and Computation Problem No. 1: In 2015, there were 233,040 Individuals living in Olongapo…

A: Let present number of people=x⇒dxdt=Rate of Expansion in number of people

Q: Consider the sequence an = 2 n n² + 7 n = 1, 2, 3, .... a. Find the first four terms of the…

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Q: The volume of the solid generated by revolving the area in the first quadrant bounded by y = e + 1…

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Q: The graph of f(x) = -² 3r is shown alongside. a Use the graph to estimate the gradient of the…

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Q: The widths (in meters) of a kidney-shaped swimming pool were measured at 4-meter intervals as…

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Q: Evaluate the integral or state that it diverges. Š In 1/8 ex dx 64e2x + 1

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Q: Find equations of the tangents to the curve x = 9t² + 3, y = 6t³ + 3 that pass through the point…

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Q: find the domains and ranges of ƒ, g, ƒ>g, and g>ƒ.3. ƒ(x) = 2, g(x) = x2 + 14. ƒ(x) = 1, g(x)…

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Q: Let s(t) = t3 - 30t2 + 18t + 47 be the position function of a car moving along a horizontal line,…

A: The given data is: st=t3-30t2+18t+47 a) Determine if the speed of the car is increasing or…

Q: rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The…

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Q: You are the marketing director for a company that manufactures bodybuilding supplements and you are…

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Q: Evaluate the indefinite integral. Stan ( tan³ (x) sec²(x) dx = +C.

A: We have to solve the given integration

Q: Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim…

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Q: Find the derivative of the following function using the Fundamental Theorem of Calculus. F'(x) =…

A: In this question we have to find the derivative of the given function using the fundamental theorem…

Q: se a calculator to approximate the degree measure (to 1 decimal place) of the angle 0 subject to the…

A: Given query is to find measure of indicated angle.

Q: Identify the inflection points and local maxima and minima of the following function. 12 y=(x²-9) 3…

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Q: Determine whether the following series converges. (−1)k+1 k⁹ ∞ k = 1 Let a > 0 represent the…

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Q: Suppose I want to use a "u" Substitution to find f cos x(sin x) dx . What should I choose for u?

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Q: For all positive numbers a and b with a>b ln(a−b)=ln(a)/ln(b)

A: given a,b positive numbers anda>b

Q: If f(x) = x³ - 8/x, find the following. (Give exact answers. Do not round.) (a) f(--/-/-) (b) f(2)…

A: Given  fx = x3-8x

Q: Suppose that a price-demand function is given by P(x) = 500- 500 - 15x. Calculate the marginal…

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Q: 4.81. Evaluate each of the following: (a) 2 mi J e³z dz, mi (b) | sinh 5zdz. ·S 0 (c) mti ! z cos 2z…

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: observer on the ground sites a plane at an angle of elevation of 42.6°. A

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Q: The accompanying figure shows the graph of a function ƒ(x) with domain 30, 24 and range 30, 14. Find…

A: We have to find the domain and range.

Q: Find the total derivative given: dy a) z = f(x,y) = 2x + xy - y² where x = g(y) = 3y² b) z = f(x,y)…

A: Topic = Derivative