n 10 2x dx te the integral (x² + 1)3 (x? + 1)-3 +c

Q: Suppose that a particular function f satisfies f" (x) = 12x? + 6x + 8, ƒ(0) = 1, f' (0) = –1. Then…

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Q: -............... ...................... ..…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Evaluate the integral using any appropriate algebraic method or trigonometric identity. 5 dx sec x-1…

A: Here we have to evaluate the given integral.

Q: 3x'e* (x* +1)* 3e a) -+C 2(x² +1) 3e* b) 2(x² +1) +C x? +3 x +1 3 c) +C .2

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Q: Verify that the function f(x) = x² – 8x + 5 satisfies the three hypotheses of Rolle's Theorem on the…

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Q: The graph of the derivative f' of a function f is shown. y = f'(x) 2 4 6 (a) On what intervals is f…

A: Let's find.

Q: Evaluat each Integral. For definite integrals, give exa Only, S X (2-5x)*dx dt

A: Topic:- definite integration

Q: *Sketch all appropriate regions or solids.* Evaluate the integral by using a Jacobian "…

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Q: For the function f, use composition of functions to show that f 1 is as given. 6. 7x-7 f(x) = =x+ 1,…

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Q: a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the…

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Q: 10 Use aepropriate substitution Ond then a trigonometric oubtitution to evaleiate the integial. dx…

A: This question can be solved using the concept of integration by substitution.

Q: dy Find dx using implicit differentiation. 5x = 2y° +7y dy dx

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Q: 5x3–x²–1 21. Which of the following is an end behavior for f(x) = %3D A. 5 B. 5x3 C. + o D.0 O D

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: a) Find dx using implicit differentiation: x + y² = 2xy³ + 1 b) Find the equation of the tangent…

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Q: 5. What is the maximum vertical distance between the line v1+2 and the parabolh v for

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Q: A/ 10 Evaluate 4/1+ cos 10x dx. A/ 10 4/1+ cos 10x dx =

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Q: f(x)

A: We will find the equation of tangent.

Q: Find the point on the line y = 1 – 6 that is closest to the origin. Give your answer in the form (a,…

A: We have to find a point on line which is closest to the origin.

Q: Suppose that a particluar funciton f satisfies f" (x) = - (4 sin(x) + cos(x)), f(0) = 3, f'(0) = 5.…

A: f"(x) = -(4sinx +cosx) ,  f(0) = 3 , f'(0) =5 now integrate the f"(x) f'(x) =4cosx -4sinx +c now…

Q: A circle is inside a square. The radius of the circle is increasing at a rate of 1 meter per day and…

A: see below the answer  and calculation

Q: fine Use FTC-1 to find the derivative of the function g(y) dz 1+ %3D

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Q: c) L{S,T sin t dt

A: Given,          ℒ∫0tςsinςdς

Q: For each of the following, solve for x. 3 1 a. %3D x+2 7-X

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Q: A driver's average speed is 50 miles per hour on the round trip between two cities 100 miles apart.…

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Q: ) Given f'(x)=12.r -4r+8, and f (3) = 1000 find f.

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Q: Show that 2x° dx = [; 2r° dx + f zr* dx + [,2x° dx %3D

A: Given that,    ∫142x2dx=∫122x2dx+∫232x2dx+∫342x2dx

Q: Show by integration that the volume of a sphere of radius r is V=4/3 πr³

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Q: d) L{e f, sin dr}

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. dx 4 - 9x2 ... dx %3D…

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Q: with the limit definition of a derivative find the derivative of g(x) = (x-1)^2 + 1

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Q: Find the derivative of the function y = (cos(x))" .

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Q: x + 5 Which of the following formats should be used for the domain of the function: f(x) = x² – 2x -…

A: Given,  f(x)=x+5x2-2x-8

Q: Evaluate the integral by interpreting it in terms of areas. (10 – 5x) dx

A: Explained below

Q: .[[bx2-5]dx = 2x³ 5]dx = 2x3- 5x + C

A: The objective of the question is evaluate the value of "b".

Q: Suppose that f is a function given as f(x) = 5x 1. Simplify the expression f(x + h). f(r + h) = f(x…

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

Q: A study of the demand for air travel between two cities depends on the airfare according to the…

A: Given query is to find elasticity of the demand.

Q: .2 y = x³ + x² у 3Dх* +x* — 4х, у — 2х

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Q: The function f(x, y) = x' – 6x + 2xy + y° + 2y +6 | Has two stationary points. Find and classify…

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Q: 25. Find the constant(s) c for which the function f(x) is continuous on (-∞,+ ∞) (c? — х2 , х<2 12…

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Q: Find the absolute maximum and absolute minimum values of the function f(t) = t – VE on the interval…

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Q: Find the determinant of the matrix, a b d e 5g 5h 5i where a b f = 7. h e

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Q: 4.1: 8) A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the…

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Q: Here is a graph of the function f. 4- 3+ 2- -3+ -4+ Use the graph to find the following. If there is…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: Consider the Taylor polynomial T(x) centered at x = 17 for all n for the function f(x) = , where i…

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Q: Question 6 (: The indefinite integral 2+1 dx equals (a) [1/x²] In(x2 + 1) (b) [1/x]In(x² + 1) ()…

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Q: Find the area of the surface generated when the indicated arc is revolved about the y-axis. y=x^2…

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Q: R is the region bounded by the given curves. R: y = x, x = 0, x = 1, x-axis Find I, Ry, Iy R.…

A: Let's find.

Q: find the derivative of f(x)=x/(x+2) using the limit definition of a derivative

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Q: Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v…

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