Give the linear approximation to: f(x) = ln x at a = e2 Approximate the numbers 7.4 (≈ e2 + 0.011) and 7.3 (≈ e2 − 0.09).

Q: Given f(x, y) decimal places. f₂( − 1, 4) = = 5x² + 2y², evalue the following to at least 4 V

A: Given: f(x,y)=5x2+2y2

Q: (1) =( 9-1², 7²²_,,sin (√1² −9)) Find the domain of the vector function, r(t) = {

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Q: The half life of carbon-14 is approximately 5568 years. If we have 250 grams carbon-14 today,…

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Q: The degree three Taylor polynomial of a function f about x = -1 is: T3(x) = 4 − (x + 1) − 4(x + 1)²…

A: Given:- T3x=4-x+1-4x+12-3x+13

Q: 2. fote-t² dt

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Q: The half life of carbon-14 is approximately 5568 years. If we have 250 grams carbon-14 today,…

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Q: Find the area of the shaded region. 2 f(x) = 10x -3x²- -x. g(x)=0 1 6

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Q: [x³ sin4xdx

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Q: Use linear approximation, i.e. the tangent line, to approximate √16.4 as follows: Let f(x)=√. Find…

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Q: Find parametric equations for an object moving clockwise along the ellipse X= = 1 beginning at (2,0)…

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Q: The midpoint of the line segment from P1 to P2 is ( - 1, 4) If P1 = (- 3, 6), what is P2?

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Q: 11 11

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Q: Answer the following questions about the function whose derivative is f'(x) = a. What are the…

A: Here we have to choose the correct option.

Q: Find the divergence of the field F. F = - 4x5i + 2y5j-8z5k OA. - 4x4 +2y4 -8z4 OB. 20x4 +10y4 - 40z4…

A: To find the divergence of the field F.F=-4x5i+2y5j-8z5k

Q: A point P is equidistant from ( - 5, 1) and (4, - 4). Find the coordinates of P if its y-coordinate…

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Q: What stated below has the same answer to 1 1/5 5÷6, 4 ÷ 5 , 5 ÷ 4 , 6 ÷ 5  Please show the work.…

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Q: Use the method of Lagrange multipliers to find the absolute maximum and minimum values of f(x, y) =…

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Q: Consider the given function h(x) = -(x-3)² +4. (a) Determine whether the graph of the parabola opens…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: Mean = Theorem can be applied to the function in the indicated 1 values of c that satisfy Rolle's…

A: The given function is; f(x)=cos2x on [pi/3, 2pi/3]

Q: (1)-(9-1²₁.sin(√²²-9)). Find the domain of the vector function, r(t):

A: To find the domain of the given vector function

Q: Given sin = and P (0) is in QII. 7 25 Find the exact value of sin 20 O 336 625 O 49 625 336 625 218…

A: To find the value of sin2θ

Q: What are of the point Coordinates the rectangular coordinates whose cynd cylindrical are (r = 2,₁ 0²…

A: We need to find rectangular coordinates.

Q: Find the radius of convergence, R, of the series. R = 1 6 ∞ I = n = 1 20 n! Find the interval, I, of…

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Q: 1. Find the vertices, foci, and asymptotes of the hyperbola and sketch its graph. (a) x² - y² + 16…

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Q: dy 8. = dx y(xy³ - 1)

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Q: A carbon sample contains 4000 atoms of radioactive element 235U. Given that 235U has a half-life of…

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Q: f(3) f(9) f(x) dx 3 9 [² x f(² 9 x f(x) dx x² f(x) dx Evaluate: = = = 8 6 16 18 = 13 9 ( − 8x + 6)…

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Q: 2ydx + x(2+x²y)dy = 0

A: Let's solve given diffential equation by using inspection.

Q: You are given the following graph of the function f(x): -Find the point where the second derivative…

A: Here we have to find the points.

Q: 1. Find the equation (in center-radius form) of the sphere whose diameter has endpoints at A(1,4,…

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Q: 6. Solve the following initial-value-problem. y" + 4y' + 3y = 0, y(0) = 2, y'(0) = -1.

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Q: Research shows that the radioactive isotope Caesium- 137 has a half-life of 30.17 years Use the…

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Q: 6. f(x) = [-x² - 6x + 8, for x < 1, 2x - 1, for x ≥1

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Q: Find by integration the area of ​​the triangle that has vertices at : (5,1), (1,3), (-1,-2)

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Q: From 1985 to 1990 a forester's grove of white pine trees grew from 80 ft to 90 ft tall. During the…

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Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

A: Given :  y" -2y' +1 = (x+1) e2x      We can solve this differential equation with the help of online…

Q: An angle measures 2.4 radians and the initial ray of the angle points in the 3-o'clock direction. A…

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Q: The cross section of a trough is a semi-circular region with a radius of 2 feet. If the trough is…

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Q: one of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.

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Q: 1. For each of the parametric curves, sketch the graph and indicate its orientation. Write the non-…

A: 1. Given parametric Functions,a. x = t+1, and y =t2,b. x = t-1, and y =tt-1c. x = tan2θ , y = sec2θ

Q: 8. Find the point of the graph of f(x) = xe-2x where the tangent line is horizontal. A(²22) C.…

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Q: If the limit does not exist, enter Ø. Sorry, that's incorrect. Try again? - 9)) = lim (sin(n+9) n→∞…

A: Given query is to find the Indicated limit.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Given query is to find the limit of the expression.

Q: Find the area under the graph of g over [-2,3]. (-x² + 5, for x ≤ 0, x + 5, for x>0 3. g(x) = =

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Q: Determine the following using partial fractions: 6x²2x-2 (e) (d) 20x + 2 8x² 14x - 15 dx dx 6x² -…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A , -2, -8) to (-2,8, -1). ter an exact answer. Ovide your answer below: isplaystyle fF.dr = 2 x X

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Q: ind the area of the parallelogram shown below 51 50 54

A: Given query is to find the are of the parallelogram.

Q: A ferris wheel is 30 meters in diameter and boarded from a platform that is 2 meters above the…

A: At t =0, Let's say the person is at the 6 0' clock position of the Ferris wheel at t = 0, and h =…

Q: Find the intervals where the function is increasing or decreasing . Use a sign chart to organize…

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Q: Determine the first two terms and the last two terms in the sum given below. 8 Σ (9k + 2) k=1

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