Calculate the length of arc of y = 2x/² for 0≤x≤1

Q: 8. Find the equation of the exponential function g(x). (No Decimals) Equation: -6 a

A: Solution ) from the graph  ( 0 , - 2) and ( 1 , 2 ) points are on the graph  Equation of exponential…

Q: dr Let A be the area of a circle with radius r. If dt = 4, find dA dt when r = 5.

A: Area of a Circle , A = πr2 ; where, 'r' is the radius of the circle .

Q: Assume that the temperature of a person during an illness is given by: T(t) = 8t/t^2+7 , where T is…

A: The answer is given in step 2.

Q: Consider the function f(x) = x² + 2x - 8 x - 3 a. Find the first derivative. f'(x) b. List any…

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Q: The position function of an object is given by r(t) = (t2, 8t, t²- 28t). At what time is the speed a…

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Q: 5 Find the derivative of f(x) = -4√x + T8 Type your answer without fractional or negative exponents.…

A: To find the derivative of the given function.

Q: у 3 2 1 -1- -2 -3 1 2 3 4 5 6 X

A: Here is the solution:

Q: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

Q: Find Ž k=0 the convergence Set for each

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Q: Find the arc-length function s(t) for the line segment given by r(t) = (9 - 9t, 40t). s(t) = Write r…

A: Given :- r(t) = <9-9t, 40t> for arc length

Q: If the relation represents a function, find the domain and range. (have it in interval notation.

A: Question: If the relation represents a function, find the domain and range. (have it in interval…

Q: A piece of cardboard measuring 10 inches by 8 inches is formed into an open-top box by cutting…

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Q: 9x²-4 :) Tax² ² (x² − 4)(x²+4) dx

A: Topic:- application of integration

Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

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Q: Find the limit. (If an answer does not exist, enter DNE.) [1/(8 + x)]- (1/8) lim X→0 X -1/64

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Q: - -5 -4 -3 -2 1 - 1 y 5 3- N 1- 1 -2H -3- 1 2 3 4 5 X

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Q: Find the area of the region between y = 6x² and y = x² + 7.

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Q: Given f''(x) = 5x - 2 and f'(-2) = Find f'(x) = and find f(1) - 4 and f(− 2) = 4.

A: Topic = Integration

Q: 2. Which expression represents the volume of the rectangular prism shown? 2x - 3 a) (2x - 3) + (3x +…

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Q: Differentiate the following function. You do not need to simplify the derivative. h(x) = (lnx) ³…

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Q: Part 1 A rectangular tank with a square bottom has base side lengths of 3 feet and a height of 10…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: (4) (d) 2-7 dx 4x-2 x²-1 (4) (e) S 7x (4x²+5)3 dx

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Q: d the equation of the tangent line to the curve y = 5x cos x at the point (7, e equation of this…

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Q: A3. SOLVE STEP BY STEP IN DIGITAL FORMAT Define g(8) for the given function so that it is continuous…

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Q: Consider the following function. f(x) = (x-8)e* (a) Find the critical numbers of f. (Enter your…

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Q: Determine the solution of the following differential equation: d²y dx² dy -8-+16y=0 dx where y(0) =…

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Q: 3. xy = a², y = 0, x = a, x = 2a.

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Q: 9. Method of undetermined coefficients y" -y = 3et ○ y = c₁e³ + c₂e²¹ + 1/{xe* -X y = ₁² + c₂e²x +…

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Q: Consider the matrix A= Calculate a31 Calculate 932 755 826 5 2 6 e 9 dh n bf a

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Q: Test Σ n 1 2" n! for convergence

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Q: The shaded region between the graphs of y x I I - 2x² + 20 and y = 3x - 15 is displayed below in 25…

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Q: 2. a) Find and fully factorise the derivative of f(x) = (2x + 1)2 using expansion and the power…

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Q: Suppose that the position of a particle is given by s(t) = 5t³ + 6t+9. (a) Find the velocity at time…

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 4x + 4 between x =…

A: Given function, y=4x+4 x=6, x=8 First we draw the diagram

Q: Find the equation of y, given the derivative and the Indicated point on the curve. dy dx y = = 2x -…

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Q: Find the limit, if it exists. Ilm Submit Answer

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Q: 18. y = 3x + 2 20

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Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

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Q: Find two positive numbers that satisfy the given requirements. The second number is the reciprocal…

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Q: 2. Find the domain and the critical points of the following func- tions on their domain: g(x) = 3x5…

A: Concept: Domain: Domain of the function is the set of all the inputs over which the the function has…

Q: 4. Consider the function f(x) and its derivatives below: f(x)=2x²-11 Horizontal asymptote(s) f'(x)=…

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Q: Differentiate the following function. You do not need to simplify the derivative. F(x) = 4e²² F'(x)…

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Q: Question 4 Use Laplace transforms to solve the differential equation: d²x di 2 + 4x = cos(21) where…

A: Topic:- application of integration and differential equations

Q: You will construct a fenced in area along the side of a building. The pen will be in the shape of a…

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Q: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration

Q: 2. d. lim f(x) = e. x-0+ f lim_f(x) = lim f(x) =

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Q: Two cars are moving towards an intersection. One car is 190 meters north of the intersection and…

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Q: Evaluate the triple integral -3pi D x dV where E is the solid bounded by the paraboloid x = 6y² +…

A: Solution is given below:

Q: Use following se k Z K-I the integral test Series to decide converge

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Q: Define g(x) to be the restriction of f(x) to the largest possible domain containing x=0 so that g(x)…

A: We have given f(x)=x-12+2You asked to solve only part(b). So we will solve part(b)In part(b) we have…