Given f(x)=√x + 2 and g(x)= x³, find ()(x) and write the domain of (x) in in interval notation.

Q: H.w: Find the Fourier series for the following functions: 1- f(x) = 1+ 1- - 2x x 2x x -π < x < 0 0 <…

A: Fourier series of f(x) in the interval [a, b] is  f(x)=a02+∑n=1∞anCos2nπxb-a+∑n=1∞bnsin2nπxb-a where…

Q: etermine the appropriate rotation formulas to use so that the new equation does not contain any…

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Q: Use part I of the Fundamental Theorem of Calculus to find each derivative, given the following f(x):…

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Q: Write an equation for the hyperbola shown in the graph. -11 744 SFE -11- The equation for the…

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Q: Evaluate the double integral x cos y dA, where D is bounded by y = 0, y = x², and x = 5.

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Q: The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0,7). One…

A: Given hyperbola, Centre (h,k)= (0,7) Vertex = (0,4) Foci = (0,2)

Q: A population of 450 bacteria is introduced into a culture and grows in number according to the…

A: Given, p(t)=4505+4t73+t2

Q: The y-coordinate of the vertex of a parabola that opens up is called the _____. minimum value…

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Q: Graph the curve whose parametric equations are given and show its orientation. Find the rectangular…

A: The graph will be  Option (B)

Q: 3 -3 f(z) dz = 0 and 7 3 f(2) dz= 7. Find [f(x) dx. -3 7

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Q: Evaluate the Integral using the following values. [x³ dx = 260, [°x dx = 10, [° dx = 2 L 122-…

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Q: Which of the following shows the expansion of 2-5n? n-0 O(-18) + (-13) + (−8) + (−3) + 0 O(-3) +…

A: To find the expansion of the given expression, substitute n=0,1,2,3,4 in the given expression.

Q: Which line has the greatest slope?

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Q: dx (a²+x²)z 1. S- 3

A: We can a valve the given integral by using the substitution x= a tanθ.

Q: Solve the initial value problem. dr-csc² 50 cot 50, 42) de 43) dy dx 3 (7) - y(0) = 6 (6 + x)2'. = 3

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Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. an = tan…

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Q: Solve the problem. 49) A private shipping company will accept a box for domestic shipment only if…

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Q: Which of the following equations represents a parabola with a horizontal axis of symmetry, vertex at…

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Q: Find the derivative of the function. y = sin (7) + √sin (6 x) y'(x) =

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Q: The kinetic energy, k, the amount of energy that a moving object has, can be found for a particular…

A: By putting the given velocity of roller coaster in the given radical function, we get our desired…

Q: What type of graph is this? A parabola An absolute value graph A hyperbola A linear graph

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Q: Solve 3 sin(2x) - 4 sin(x) = 0 for all solutions 0 < x < 2π x= Give your answers accurate to at…

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Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

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Q: Graph the curve whose parametric equations are given and show its orientation. Find the rectangular…

A: To plot the graph of the curve with the given parametric equation, first  find the x and y values…

Q: 6) y = (4 - x2/3) 3/2 from x = 1 to x = 8

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Q: Find the limit. 54) lim (lnx)/x X→∞

A: We need to find limit.

Q: Solve the problem. 57) From a thin piece of cardboard 10 in. by 10 in., square corners are cut out…

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Q: Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the…

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Q: The graph of a function is given. -4 -2 X I 4 2 -21 -4 2 4 (a) Determine the interval(s) on which…

A: We can find the answer as below.

Q: Determine all Horizontal Asymptotes. x²-2x+1 x³+x-7 50. f(x)=. 51. f

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

Q: Find the equation of the parabola described below. Find Kthe two points that define the latus…

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Q: 6. (y -x + xy cot x) dx + x dy = 0 Answer: xy sin x = C + sin x - x cos. x.

A: We have to solve this question with exact formulation.

Q: This exercise uses the radioactive decay model.. The half-life of radium-226 is 1600 years. Suppose…

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Q: What is the equation of the rational function g(x) and its corresponding slant asy -10-9-8 O O O 7…

A: Given: Graph:

Q: A-Evaluate the following double integral - (x² + y²) dy dx fo

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: Write an equation for the hyperbola shown in the graph. 747 7-112

A: We know Standard Equation of vertical hyperbola y-k2a2-x-h2b2=1 Here Center h,k  Equation of…

Q: Assuming the pattern continues, what is S₁2 for the series -8-15-22-29 -...? -565 -85 -510 O-558

A: Option d is correct.

Q: Water is leaking out of an inverted conical tank at a rate of 14000 cubic centimeters per min at the…

A: Given that, the leakage rate is 14000 cubic centimeter, the height of the tank is 12 meters and…

Q: udx + (1 - 3u)x du = 3u du.

A: I have stated the used formulas in the solution

Q: A polynomial P（x) of degree seven has zero of 2-i and 4+i, the graph of P(x) has how many x-ints

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Q: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: x3* lim x-03-1

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Q: Find an equation for the hyperbola described. Graph the equation Center at (-1,-4); focus at…

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Q: a=, b= a) a-2b b) a + b c) à b d) The angle between a and b =) Find all vectors which are twice as…

A: We need to solve vector problem..

Q: The graph shows the rational function f (x) and the logarithmic function g(x). f(x)…

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Q: 97 Find the following percentage. oon ai show my wade-VOIT 16% of 79-264 siri) 98. Find the…

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Q: Identify the equation without applying a rotation of axes. 6x² - 10xy + y² +10x+7y-1=0 Choose the…

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Q: Determine the appropriate rotation formulas to use so that the new equation does not contain any…

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Q: the blank(s) provided. 9. The y-intercept of the function f(x)=4(2) is 10. To the nearest hundredth,…

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Q: Determine whether the series converges or diverges. ∞ 7" 5 + 12" n = 1 The series converges by the…

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