12. The slope of the curve y = x2 - e-* at its point of int A. -In 2 В. C. 2+In 4 D.

Q: Plot the set 1,0, on the number line. Round to the nearest tenth where applicable. Answer How to…

A: We can plot the points on the number line as below

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Q: find the equation of the tangent and thhe to the Pollo wing cunve uhen x = 1 (2x2- Ja)2 normal .

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Q: Q38: If y = e2x sin 5x, then which of the following is true? (a) y" – 4y' + 30y = 0« (b) y" – 4y' +…

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 2et…

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Q: 1) Ifféx) =x + 5 and g(x) = x² -3, then find g(Ư(0) . 2) Iffés) = secx, and g(x) = L, then find…

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Q: Compute the work required to stretch a spring from 4 to 12 cm past equilibrium, assuming that the…

A: the equation to find workdone is; workdone =(1/2)kx^2   given,  stretching the string from 4 to 12…

Q: 0.2 0.4 0.6 0.6 1 f(x) 32 24 12 8. 10

A: Here we have to compute L5 using the given values.

Q: /9-x² dx. Use trigonometric substitution. x2

A: This question is related to indefinite integration, we will we will solve it using given…

Q: Sketch and determine the center, foci and vertices of th equation of x2 (y-4)2 + 36 = 1. 49

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Q: Strontiun1-90 nas d nall-lire of 28 days. (a) A sample has initial mass of 50 mg. Find a formula for…

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Q: Using Integration By Parts, Vx In 2x dx= uv- Jv du- Find u v- du- 3 x/x In 2x- Vx dx 2 O 2 xVx In…

A: The given integral is: ∫xln 2x dx

Q: 2x, The graph X;+1° (Continue) Consider the discrete time dynamical system X†+1 = of the updating…

A: We have to find the positive fixed point stable or unstable.

Q: YA Y= 5X-x² 2. (4,4) Y= x Find the Alea Of the shaded hegion

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Q: 3) Convert the following polar equations to rectangular equations. 1 a) r = b. r=4 4 cos 0-3 sin 0

A: (a)r=14cosθ-3sinθSince, x=r cosθ , y=r sinθso,cosθ=xr , sinθ=yrsubstitute in the given polar…

Q: Consider (2x2- x² + x +2 x4 + x3 C D B + dx = dx find A+B+C+D- + x+1 O 3 O 2 O 4 O 5

A: Topic:- partial fraction

Q: USING A- V2P de, FIND THE AREA OF ONE PETAL OF THE ROSE DEFINED BY THE EQUATION 3cin(2B)

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Q: Question 1 Which of the following are subspaces of R ? Choose all correct answers. {(x, y, z) E R³ |…

A: Only option 1 and 3 are subspace of R^3

Q: Question 8 Saved If limx→a f(x) 8(x) = 1 and limr-→a g(x) = 0 then, we must have limx→a = True False

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Q: Use a graphing utility to graph the function and find the absolute extrema of the function on the…

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Q: Decide whether the limit exists. If it exists, find its value. fx) 3+ 2+ -2 -1 3 X -1+ -2- 1) lim…

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Q: 00 n +7 Use the ratio test to determine whether>. converges or diverges. 7" n=3 (a) Find the ratio…

A: To find whether the given series converges or diverges using ratio test.

Q: Find any critical numbers of the function. (Enter your answers as a comma-separated list.) g(x) = x6…

A: For critical numbers, Put g'(x) = 0 and solve for x.

Q: 2x+11 3 1 dx evaluate Consider x² + x-6 dx- x+3 x-2 x+3 X-2 x-2 In +C |x+3 |(x-2)³| In x+3 |x+3 +C…

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Q: 1 2. (33.6) Use the building block > a", |r| < 1, to find a power series representation 1–x n=0 for…

A: Solve the following

Q: Find the general solution of the differential equation. y(4) – 6y(3) + 9y'" = 0 ... y(x) =

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r= 4 cos 2t and e = 5t

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Q: dx 3 sin e+C = Using Trigonometric Substitution 3 express the answer in terms of x. (x²+ x + 1)7

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Q: ul = 7,0 = 25

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: и + Use the ratio test to determine whether > converges or diverges. п! n=12 (a) Find the ratio of…

A: Here, the given series is: ∑n=12∞n+5n! Let, an=n+5n!; n≥12

Q: Find the average value of f(x)=9x+1 over [4,9]

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Q: find S- とx 1-COS2X

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Q: 104. x + 4xy – y³ = 6

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Q: Evaluate the integral. .V3/2 35x2 dx V1- x2

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Q: 2. Sketch the region and find the area of the region bounded by y = -x? + 9 and the x-axis.

A: The region is bounded by the curve y=-x2+9=-(x-0)2+9 and the x-axis.

Q: Consider the function on the interval (0, 27). f(x) = sin(x) cos(x) + 8 (a) Find the open…

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Q: Evaluate the integral cot5 x csc3x dx O Lesc" x - ese" x + cse" x - c 2 csc' x + 5 글csc3 x + C 1 X +…

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Q: 1) Plot the following points on a polar coordinate system. a) (1,45°) b) (3.) 2) Convert the…

A: In polar coordinate r,θ,if  r is negativen then add π to the angle . Note : As per our Guidelines ,…

Q: 1. A business wants to manufacture a huge closed box with a square base a square top and rectangular…

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Q: 48. f(x) = (x – 4)(x² + 6x – 1), (0, 4)

A: We need to find the equation of tangent line for fx=x-4x2+6x-1 at point  0, 4

Q: Find the general solution of the differential equation. 121y(3) + 132y" + 36y' = 0

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Q: What is wrong with this calculation? 1 dx = In 1- In 1 = 0 %3D Choose the correct answer below. 1. O…

A: Given expression is                                         ∫-11 dxx = ln x-11 = ln 1 -ln 1 =0    We…

Q: •4 b (3x – 4)° dx = || f(u) du where (enter a function of x) = n dx (enter a function of x) — пр a =…

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Q: 3s+10 W(s) = s(s-8)(s-6)²

A: To solve the following problem

Q: Which of the following functions is the derivative of „sin(x) f(x) : = X sin(x) cos(x) xsin(x)…

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Q: Find the slope of the tangent line to the graph at the given point. (x² + y?32 = 4x²y, (-1, 1)…

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Q: Find the derivative of the function. y = 3 x tanh-1 x + 3 In/1 - x2 y' =

A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

Q: Write an equation of the tangent line to the graph of y = f(x) at the point on the graph where x has…

A: Solving

Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at…

A: Here we will find the smaller and larger distance values,

Q: ind the points of inflection of the graph of the function. (Order your answers from smallest to…

A: Here, the given function is: f(x)=x(x-4)3 So,…