Evaluate lim x - 4 3 O O 3 1. 4 3 2 3 (2x + 1)² 3x² + 8x - 3

Q: ) identify the technique of integration most appropriate b.) Find the average value

A: Here we have to use the concept of integration

Q: Question -3x-13 Given that s(x) = find (s-¹)'(8) using the I x+8 Inverse Function Theorem. Note that…

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Q: 3. Evaluate the double integrals. -1/2 (a) [fx(1+ y²) d4; R is the region in the first quadrant…

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Q: Evaluate the integral f sin²x cos³xdx.

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Q: Əw 1. If w=x" f() show that x ax +y Əw ду = nw where n = integer.

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Q: Determine dy/dx given that: y = sinx - sin³ x O cos³x O cos x sin² x O sin³ x O - cos³ x -

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Q: 24\x² dy_ (xy + y ² ) d x = 0

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Q: Given the function f(x) = x² + Draw a sketch of the graph of f. 16 X x>0

A: Solution is given below:

Q: The marketing research department of a computer company used a large city to test market the firm's…

A: This question can be solved using the concept of maxima and minima.

Q: Solve the following differential equations of d²y dx² +9y=2e³x +18x+18

A: The given differential equation,      d2ydx2+9y=2e3x+18x+18

Q: Determine which of the graphs below have Euler circuits. Vo Vg VI 3 m (US S 5 e6 4 33 V3 Ug (US 27…

A: Euler circuit: An Euler circuit starts & end at same Vertex Here in the given problem we have to…

Q: 1 Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

A: We have to find the required plane

Q: QUESTION 16 hexagons can form a tiling of the plane. A. All OB. No C.Some

A: Option (C) is correct.See below the answer and explanation

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

A: you are driving a car away from home.your velocity t hours after noon is given by,…

Q: dx 5 - 2x Evaluate: S O2 ln |5-2x + C -2 + C 5-2x O -1 2(5-2x) + C On 15 - 2x + C

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Q: (I) Find the critical points of the function f(x) = x + x² + 1

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Q: ind the equation of a line that passes through A(1,-1) and is perpendicular to the line (x,y) =…

A: The equation of a line that passes through A(1,-1) and is perpendicular to the line…

Q: determine the instantaneous rate of change for the function f(x)=7^x + 9log(x^x) at x=4

A: This question can be solved using the concept of derivative of a function at a point.

Q: e The median weight of a boy whose age is between 0 and 36 months can be approximated by the…

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Q: The measurement of the side of the cube is 6 cm long. If this length has an error of 1/12 cm. Find…

A: Topic = Derivative

Q: f(x) = x² + 16 X 6 0<x

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Q: ind area bounded by y = 0, y =√x-x² using double integration.

A: We have to find area of given region.

Q: For which of the series below the Integral Test can be used to determine whether the series is…

A: Recall the integral test:If fx is continuous, positive, decreasing on the interval k,∞ andfn=an…

Q: If f(x) = 2x²e*, find f'(1). 2e 6e 0 4e

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Q: Find the Wronskian of the functions f(t) = 3et sin(t) and g(t) = et cos(t). NOTE: Your answer must…

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Q: 11. A plate in the form of a parabolic segment of base 12 m and height of 4 m is submerged in water…

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Q: Find the acute angle between the line joining A(1,2,3) and B(5,1,7) and the plane containing point…

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Q: -1 Let f(x) = tan-¹ e²². Find f" (x).

A: The solution is given below

Q: 3 Find the area between the curve of X = and the y-axis on the interval [2, 5]. 2.749 3.296 4.159…

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Q: Q6A)If y sin find Zxy.

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Q: Which of the following integrals is convergent? Select the correct answers. .24 0 of OP 0 2 X dx dx…

A: We have to find which of the following integral is convergent. (a).…

Q: Find the domain of the following function. 5 f(x) = 81-x² The domain is (Type your answer in…

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Q: Evaluate the integral. V3 /1 v3 + 3v6 3v6 d v4 dv

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Q: a dy Find given y = 4 In da

A: The given function,   y=4x lnx

Q: 1. If f(x) dx = 3, evaluate [[1 + 21(x)] dx using the properties of interga 2. If f(x) dx = -2 and…

A: As asked we can answer question no 1 and 4 as below.

Q: Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the…

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Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y…

A: We have to solve above given graph for volume.

Q: Find the volume bounded by: x² + y² + z = 16 and z-x² - y² = 8

A: Concept: If a solid S is bounded by a surface, as in rectangular coordinates,  z=f(r,θ) as well as…

Q: TC d) x² sinx dx e) ₁x² Inx dx f) so xe dx

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Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

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Q: In the year 2000, the population of a small city was 48,000. The population grows at a rate of r(t)…

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Q: Write the inequality in interval notation and graph the interval. -5<x<5 The interval is 0

A: Use interval notation

Q: 19 Can a graph with three vertices of degrees 2, 1, 4 exist? Yes No

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Q: [x√x + 1dx

A: Here we have to integrate I=∫xx+1dx

Q: A loan, amortized over 10 years, is repaid by making payments of $1,000 at the end of every month.…

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Q: The manager of a restaurant found that the cost to produce 100 cups of coffee is $10.55, while the…

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Q: A conical vessel full of water is 16 ft across the top and 12 ft deep. Find the work required to…

A: Given: Volume of the conical vessel=13π r2h          where r= radius of vessel                    h=…

Q: Find the absolute minimum and absolute maximum of the function f(x) = (x2 − 1)3 defined on the…

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Q: d²y dy 2. +4 + 4y = 0, when x = 0, y = 1, y' = -1 dx² dx

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