Evaluate CD dx where C = x and D = e-4. Which integral techniques did you use? Please explain.

Q: Suppose that f(x) = g(h(x)). In each part, based on one of the functions provided, find a formula…

A: Given: (a) If , then to find .(b) If , then to find .Note: Since the student has posted multiple…

Q: Find ƒ'(−1) if 4x( f(x))² + 4x³ƒ(x) = 0 and ƒ(−1) = −1. ƒ'(−1) =

A: we need to find out the f'(-1).

Q: 6. Calculate the domain, intercepts, horizontal and vertical asymptotes with limits, intervals of…

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Q: (7.3) Find the inverse Laplace transform, L-¹ 1 2s + 14 s² + 2s + 10.

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Q: 2. Find the critical numbers and the open intervals on which the function is increasing or…

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Q: 2. Use g(x) = 1 + x on the interval [1, 3] in this problem. X a. Show that The Mean Value Theorem…

A: Mean value theorem:a) If  f(x) is continuous on[a,b] and f(x) is differentiable on (a,b) then there…

Q: Find the equation of the line tangent to the graph off at the indicated value of x. f(x) = 9+4 Inx;…

A: Given,

Q: Find the indefinite integral using a table of integrals and using the given method. (Remember to use…

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Q: A rectangular area adjacent to a river is fenced​ in; no fence is needed on the river side. The…

A: Consider the figure Let x be the length of one of the sides perpendicular to the river.Let y be the…

Q: Convert the point from rectangular coordinates to spherical coordinates. (-1, 2, 1) (p, 0, q)…

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Q: Given the function g(x): = 3x - 2 X 2 a) Find the interval on which g(x) is increasing/decreasing;…

A: As per the company's guidelines, we are supposed to answer the first three sub-parts for you, Kindly…

Q: dy. Simplify your answer. dx y = x³(1-x²) Calculate

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Q: This exercise is based on the following table, which lists interest rates on long-term investments…

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Q: Find the values of x for which the series converges. (Enter your answer using interval notation.) 00…

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Q: Determine whether the geometric series is convergent or divergent. 00 2 πη n = 1 convergent O…

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Q: Find the critical numbers of the function. (Enter answers as a comma-separated list) g(y) =  y − 5…

A: The function is given byTo determine: The critical number of the function.At the critical point, the…

Q: 4. Find the limit of the following sequences. You can use any method you choose but make sure to…

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Q: The function f(x) is graphed below. Determine whether the degree of the function is even or odd and…

A: Consider the graph

Q: Answer the following questions about the sphere whose equation is given by 1. Find the radius of the…

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Q: m 4. Consider sin x cos" xdx. (a) How do you evaluate fsin" x cos" xdx if m is odd? (b) What if n is…

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Q: How long (in years) will it take a $200 investment to be worth $300 if it is continuously compounded…

A: The Formula for compounded continuously where P is the amount after time t  is the initial amount…

Q: Determine the inflection point of the following cubic: The inflection point is at (x, y) = ( [ f(x)…

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Q: The rectangular coordinates of a point are given. Plot the point. (-2√/2,-2√2) 2 4 X -4 -2 4 X

A: The given rectangular coordinate isSo here we have,

Q: Find the first partial derivatives of the function. || f(x, y) = gy

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Q: Find the first partial derivatives of the functio f(x, y, z) = xyz + xy2 + y2² + zx fx =

A: Given,

Q: Convert the point from rectangular coordinates to spherical coordinates. (-1, 2, 1) (p, 8, 4) = ( X

A: The point in cartesian coordinate is given byTo determine: The point in spherical…

Q: Differentiate the following function. f(x)=9-4x+5ex f'(x) =

A: Given,

Q: (c) This graph is a rose curve (d) π/2 π/2 2 3 4 5 6 7 8 I with equation 0

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Q: Consider the following function f(x) = 7x ln (6x). Determine the following: (a) The open interval on…

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Q: The velocity of an object is shown in the graph below 5+ 4 Velocity (m/s) N لا 3 1 1 pasij 3 Time…

A: The velocity of an object is shown in the graph below.To calculate the total distance traveled over…

Q: 2x Use the function f(x) x² + 5 (a) Find the interval(s) on which f(x) is increasing. Number of…

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Q: USE THE GIVEN TEST TO DETERMINE THE CONVERGENCE THE GIVEN SERIES. OR DIVERGENCE OF INTEGRAL TEST a)…

A: The given series

Q: DECIDE WHETHER THE GIVEN SEQUENCE OR SERIES IS CONVERGENT OR DIVERGENT. IF CONVERGENT, ENTER THE…

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Q: ints) Determine if the improper integral is convergent or divergent. Eval- e integral if it is…

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Q: 28. IM. IM. M. sin n 2" 30. (-1)-1. 32. (-1)". (-1)" n-2 n ln n 34. Σ n n² + 4 n √n³+2 Tod 29. 31.…

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Q: Let lim g(x) = 3 and lim h(x): = 3 x→4 x→4 Determine the value of the limit h(x) lim x+4 x + g(x)…

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Q: Suppose that p(x) = anx" converges on (-1, 1], find the interval of convergence of p(6x - 4) . x= to…

A: If a series P(x) converges on the interval (−1,1], we can determine the interval on which the power…

Q: , by using a half-angle formula, find

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Q: (b) π/2 Jo 1 2 3 4 567 This graph is a rose curve , with equation 0

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Q: Use graph below to calculate the following: (a) f(f(2)) = (b) g(g(2)) = (c) f(g(4)) = (d) g(f(4)) =…

A: A graph of the functions  and  are given.The aim is to find the composite function values  and .

Q: Let y = f(x) be given by the graph below: -6 -5 -4 -3 -2 -1 -4 -1 02 6 04 3 1 Out of the options…

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Q: 8 2. a) Differentiate the function Q(p) = -2³√/p³ (e²-√³) b) Hence or otherwise, determine Q'(1).

A: The given function

Q: Which linear function is represented by the standard form equation below? 4x + 5y=40 A f(x) = -x+8 B…

A: the standard form of equation is 4x+5y=40

Q: Find an equation for the conic that satisfies the given conditions. ellipse, center (-3, 3), vertex…

A: Given that ellipse  with center  ,vertex , focus From the given data  the x coordinate of vertex,…

Q: Test the series below for convergence using the Ratio Test. (−1)®g2n+1 (2n + 1)! n=0 The limit of…

A: The ratio test:

Q: Find the Laplace transform, L{t² sin(t)}.

A: To find the Laplace transform, .

Q: Determine whether the geometric series is convergent or divergent. 36 216 7 + 6 + + 7 49 O…

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Q: The value of c that satisfies the Mean Value Theorem on the interval [0, 5] for the function f(x) =…

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Q: A closed box is to be constructed so that its base length is three times the base width and is to…

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Q: The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the…

A: Given,Area of a triangle, =88 Altitude of a triangle, The rate of increase of altitude of a…