4) The area under the curve defined by the positive function f (x) on the interval [2, 6] is known to be 34. What is the average value of f (x) over the interval [2, 6]?

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A: Concept: Newtons forward difference interpolation method: Extrapolation is the process of computing…

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A:

Q: Q3)Evaluate the following integral by using Trigonometric Substitutions Method. dx = √√√9x² +9 y =

A: Let's solve integration by using trigonometric substitution.

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Q: 33. " +9y sin 2x; y(0) = 1, y' (0) = 0 34. y" + y = cos x; y (0) = 1, y'(0) = -1 35. y" - 2y + 2y =…

A: Given: y(3)-2y''+y'=1+xexAuxilliary equation: m3-2m2+m=0Therefore, m=0,1,1Complimentary…

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Q: Determine whether the function defined is one-to-one. f(x)=√/32-x² -X www Is the function…

A: I am going to solve the given problem by using some simple calculus to get the required result.

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A: We have to find the domain

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A: The value of the limit is when x tends to 0 for the function (cos(x))cotx

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A: We have to determine domain

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Q: Q6) Find the Area bounded by the curves y = √√x and x = 2y-y² ,with sketch.

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Q: 7,000e0.1x dx   Find a substitution to rewrite the integrand as 70,000eu du. u=     du =        dx…

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Q: Evaluate the following integral by using Odd and Even Powers Method: y = [₁ cos5 (1x) dx

A: We will evaluate the given integral by using odd and even power method in the following step.

Q: Find the limit, if it exists. (If an answer does not exist, 3 - xy ху lim (x, y) → (2, 1) x² +2 +9y²

A: We will apply the limits.

Q: Ho Find (dy/dx) for: tanh-¹(x y) + e(x+y) 5 cos(y)

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Q: Evaluate the following integral. 1 tan (√3x) 1 2 (3x)² +(3x)² - 13 0 MIN 3 dx

A: Here we have to find the integral

Q: dx 4 sin x 3 cos x

A:

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A: This question is related to rate of change, we will solve it using given information.

Q: c. p> 1 7.One of the following sequences is divergent sequences a. 3n² + 2n n5 + 7 n! b.{-1)".…

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A: Here, the given model is for the population of a certain inner-city area after t number of years:…

Q: 1. So letet Jo 1+ e* t -dx

A: The given integral,        ∫01ex1+exdx

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A: We know, Average velocity =Total DisplacementTotal time

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A: topic- average value of function over interval

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Q: Find the area bounded by the curve y = x + 3 and y = x²+x-13, from x=1 tox=3. a. 23 sq. units b. 20…

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Q: 4) The area of the surface generated by revolving x= y²-1, 1≤ y≤ 2 about x-axis is S=...

A: To find the area S of the surface generated by revolving x=y2-1, 1≤y≤2 about the x‐axis.

Q: Find the area of the region between f(x) = x² + 2 and g(x)= x - 1 on the interval [-2,2]

A: The functions are f(x)=x2+2  &  g(x)=x-1

Q: 2. Find y' if y = 7* (log4 x)⁹.

A: The given function y=7xlog4x9

Q: 14. The Integral:√4-3x² a. cos²0.de dx, can be transformed into : b. 2f cose.de c. 2 f tano.de d. 4…

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Q: x2 dx+(x3+y6+2y5)dy Give an implicit solution

A: we need to find out the solution of the differential equation.

Q: Provide your answer below: Domain in interval notation is Range in interval notation is

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Q: By using Euler method, Solve these questions 3.3 2 2 XD² + 2XD + XD=Y=6

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Q: Use the One-to-One Property to solve the equation for x. (Enter your answers as a comma-separated…

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Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: 1 If f(x) has an inverse function f-¹(x), could either the graph of for the graph of f-¹ be…

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Q: Evaluate the 106 -20 (-7m+300)

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A: We need to find dy/dx.

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A: