Let f(x) be the following piecewise function x² + 1, 1 (x+1)² 2x-3 x²+1 f(x) = if x < -1 if -1 < x < 1 if x ≥ 1

Q: Use Newton's method to approximate the given number correct to eight decimal places. √47 1.89969104…

A: Use Newton's method to approximate the given number correct to eight decimal places.476

Q: 8²f Let f(x, y) = cos(xe¹²) + cos(x + ey²), find əxəy O a. O b. O C. O d. -2yey² (sin(xe¹²) - x…

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Q: Divide. (8x³-4x²-12x+15) + (2x-2) Your answer should give the quotient and the remainder. Quotient:…

A: Please see the below picture for detailed solution.

Q: VALUE INSIDE THE CIRCLE cos² x Yp = D²+1 For given particular integral multiplying and dividing by 2…

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Q: 8 26 Type your answer without fractional or negative exponents. Use sqrt(x) for √√T. Find the…

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Q: A) Let g(x)=x² (5x+24 (2x + 8 a) lim x-1 b) lim X-0 a) lim g(x), lim g(x) x--3 x-0 B) Find the…

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Q: Rewrite the equation in exponential form.   ln(b)=n

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Q: the equation of the tangent line to the graph of the function f(x) = √√4x³ + 5 at V

A: Topic:- application of derivatives        Slope of tangent line is first derivatives of curve at…

Q: Find curl(F x G) = V x (F x G). F(x, y, z)= i + 7xj + 6yk G(x, y, z) = xi - yj + zk

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Q: 9. Give a geometrical interpretation of the intersection of the planes with equations x+y-3=0…

A: Give a geometrical interpretation of the intersection of the planes with equation. x+y-3=0 y+z+5=0…

Q: Suppose 150 trout are seeded into a lake. Absent constraint, their population will grow by 35% a…

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Q: The area of the region inside the circle r = 6 cos 0 and outside the cardioid r = 2(1 + cos), a > 0…

A: Given: the circle r =6 cos θ and the cardioid r=2(1+cosθ )

Q: force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the Give the…

A: This is a problem related to 2nd order differential equation of the newton's law of spring motion.…

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

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Q: Find the general solution of the given higher-order differential equation. y"" + 4y" - 9y' - 36y = 0

A: Follow the procedure given below.

Q: Find by implicit differentiation, given that x²y – 4y5 = -8. Your answer could involve both x and y.…

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Q: Use the rational zeros theorem to list all possible rational zeros of the following. g(x) = - 10x³ -…

A: The given polynomial gx=-10x3-8x2+8x-4

Q: Find the equation of the tangent line to the curve at the given point. \\ y = 1 + 2x − x³, (1, 2) y…

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Q: A company's revenue from selling x units of an item is given as R = 1000x - x² dollars. If sales are…

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Q: Problem 2.1 Find the vertical asymptotes of the function Then graph the function. Y x² +1 3x - 2x2

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Q: EX: Show that d² = 2πi where c is a unit § Z circle. C:1Z1 =1 Sol: ie Z= re io dzir e do 24 io ixe…

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Q: 7. Determine the intersection, if any, of the planes with equations x +y-z+12=0 and 2x + 4y - 3z…

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Q: Əw Find Ət using the appropriate Chain Rule for w = x² + y² + z² where x = 10rsin(s), y = 10tcos(s),…

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Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: 3X y 2y = 4y + 8y = 2³x + 8x² 2X <-2X Ans: y = ₁2x + ₂xe + cze -25 X -3X 2 —=== ² + x + x + 1²/2

A: This is a problem related to ODE. Based on the general formula and concept we will answer.

Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

A: We want to find the area of region bounded between the given curves

Q: Determine whether the given set of functions is linearly independent on the interval (-∞o, co).…

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Q: Let f be the piecewise function i. 11. f(x) = (x³ + 6x² + 8x x + 2 x 1 Sketch the graph of f. Based…

A: Solution is given below:

Q: 2. Simplify the following logarithms and If possible, write the following as a single logarithm. 1…

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Q: 1 r= 1 + cos !

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Q: If f(x) = 4x² - 5x + 5, find f'( − 3). Use this to find the equation of the tangent line to the…

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Q: A force of 400 newtons stretches a spring 3 meters. A mass of 40 kilograms is attached to the end of…

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Q: Given differential equation -3x y"-sy" -4y' + 8y = e +8x9 (D³ - 20² - Auxilary equation m²³²³ - 2m²²…

A: We have to explain the particular solution.

Q: Find the general solution of the given second-order differential equation. 20y" 11y' 3y = 0 y(x) =

A: The given differential equation is: 20y''-11y'-3y=0   So, we can also write as; 20D2-11D-3y=0 The…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: We have verified that x² and x are linearly independent solutions of the following second-order,…

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Q: The equation implicitly defines z as a function of t. Find dz dt +² 22 - sin (5 z) = -8

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Q: I'm not sure how ti find the position vector. Could you please give me some instructions? Thank you.

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Q: The tank shown is full of water. 3 m E. 8m 3 m (a) Find the work required to pump the water out of…

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Q: 19j isn't even an option... neither is your choices of + and - Please review possible answers and…

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Q: If z = 5x2 + y2 and (x, y) changes from (1, 2) to (0.95, 2.1), compare the values of Δz and dz.…

A: We have to compare the values of Δz and dz.

Q: Use Res(f(z), zo) lim (z-zo)f(z), Res (f(z), zo) = 2-20 to find the residue at each pole of the…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The linear operator that annihilates anxn+an-1xn-1+....a0 is Dn+1 The linear operator that…

Q: Find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: HOW DID HE GET THE VALUE INSIDE THE CIRCLE cos² x D²+1 For given particular integral multiplying and…

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Q: Find the equation of the tangent line to the graph of the function f(2)=sin(7√) at the point (²,0).…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  so we can take

Q: Step To sketch the graph of f(x) = 4x - x², first construct a table of values by evaluating the…

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Q: 12. Let x be a positive real number and f(x) = log₁0x. Then f(10-x-2) is equal to: I1 f(x) B.…

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Q: Write the following equation in logarithmic terms. Do not simplify your answer. e5 = 4.5 Answer ||…

A: we have to write the given function in logarithmic terms . For this, first we should know some…

Q: 8 9 10 11 e centroid of the region displayed in the graph.

A: Topic:- Geometry