1. What rule is applied in the following given? * Dx (-13) = 0 Power Rule of Differentiation Product Rule of Differentiation O Constant Rule of Differentiation O Sum Rule of Differentiation

Q: COS X 6. y = x What is the appropriate formula? dx Solution:

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

Q: Determine whether the series converges or diverges. 4n³ n²-4 n=2

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Q: 2. y = x² sinx What is the appropriate formula? dy Solution:

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Q: 9 Use the second derivative test to find the location of all local extrema in the interval (4) for…

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Q: Use a computer algebra system to graph f and to find f' and f". Use graphs of these derivatives to…

A: A function is increasing on an interval if for every point on that interval the first derivative is…

Q: For two exclusive events A and B, P(A) = 0.2 and P(A U B) = 0.65 If the given information is shown…

A: Solved below

Q: Calculate the work expended when a particle is moved from 0 = (0,0) to Q = (4,4) along the segments…

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Q: Sketch a function that is continuous on (-∞0,00) and has the following properties. Use a number line…

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Q: 32 Question * (3 Points) The proper transformation for sin²x to make the f sin²x dx readily…

A: substitution

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 6x²y²j

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Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: Find the length of the parabolic segment r= 6 1 + cos 0 The length is. (Type an exact answer, using…

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. a. So f(x) dx…

A: Let's find.

Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m − n)] dx…

A: Let's find.

Q: If F(x) = f(t) dt, where f is the function whose graph is given, which of the following values is…

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Q: 29. aj = x, a₂ = x+3 30

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Q: Find the area of the region under the graph of f on [a, b]. f(x) = x² - 6x + 13; [−1, 2]

A: To find the area of the region under the graph of f(x)=x2-6x+12 on the interval [-1,2].

Q: Σ n=2 7 n(In(n))*

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Q: Evaluate the following: 1) S x² √1 + x dx

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Q: 3. Evaluate the double integral: ²₂2(x+3) dy dx 4. Evaluate the triple integral: ₂ dx dy dz Z

A: Topic:- multiple integration

Q: The f2e4t sec2e4t dt is {A} = = tan e 4t + C {B} = sec³e4t + C 16 {C} /e4t tan e4t + C {D} et…

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Q: 3-2ey 3y-zey dy is Зу-2еу {A} - In|3y - e²y|+C The f

A: we have to find the integration.

Q: If |ū| = 4, |v|=5, |ū-v=6, determine |ū+ v.

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Q: 10. | x³(lnx+1)8x* dx

A: To evaluate the integral: I=∫xx(ln x+1)8xxdx=∫8xxxx(ln x+1)dx

Q: Evaluate the iterated integral. [²1²₂(x² - y²) dy d dx

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Q: Decide whether the integral is improper. 1,01 In(x5) dx

A: We are asked to find whether integral is proper or improper

Q: 7. ft³10t+-3 dt

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Q: Plot each of the given complex numbers in an Argand diagram and label all the necessary parts. Also,…

A: Since you have submitted multiple questions, according to Bartleby policy I'll solve the first…

Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent.…

A: From the given series we have to check the convergent and divergent of the series.

Q: How many terms of the series do we need to add in order to find the sum to the indicated accuracy? ∞…

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Q: Determine whether the improper integral diverges or converges. S™× x²e-x dx converges diverges…

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Q: 2. Find each indefinite integral CS Searned with (278x²) da eamscanner 2.5

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Q: Find the laplace transform of f(t) = 6t³ + 4t² 3 F (s) = F (s) F (s) = F (s) = F (s) F(s) = -85³ +…

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 6x + 17 between x =…

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Q: Of all rectangles with a perimeter of 10, which one has the maximum area? (Give the dimensions.)

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Q: Je-2x sin 2x dx

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Q: Find the curvature of the curve r(t) = (-4t, - 3t², 5+³) at the point t = − 2. Give your answer to 2…

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Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4.

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Q: B. The maximum value of f(x) is h. OC. The graph of y = f(x) is a parabola. D. If a 0, then f has a…

A: Topic:- calculus

Q: Problem 4. Part (a) Part (b) 5 ln(3-x) = 4 Do both parts. Write the sum using sigma notation:…

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Q: 55. the sum of the first 80 positive integers 56. the sum of the first 120 positive integers

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Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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Q: An equation of a conic is 5 r = 3+2 sin 0 Identify the conic, find the eccentricity, write an…

A: A conic section with a focus at the origin, eccentricity e, and directrix at x=±p has polar…

Q: Q/ By uesing chain rule Find du de For this functions E² +1 x² + y² X x = tanzt, y = e 2x a = / 11 ?

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Q: Evaluate the following: 1) f sin x sin(cos x) dx

A: Integration

Q: 8) Find the unit tangent and unit normal vectors T(t) and N(t) for r(t) = (t, t², t²).

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Q: find dy/dx of each equation using implicit differentiation. a. y4 -2y2x2 + 3x2 = 0 b. (x + y)3 =…

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Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: 6. Evaluate any 5 of the following 6 integrals. (a) 12 dx 1 (b) (c) cos(50) de (e) [x²e² dr (d) (f)…

A: To evaluate the following integrals.d ∫xx+1 dxe ∫x2ex dxf ∫arcsin x dx

Q: 1. y = cost-sin 4 t

A: