Find the length of the curve. 8(1) - (48, 1², 12³). r(t) = Osts 1

Q: Find the arc length of the curve below on the given interval by integrating with respect to x. 3 =…

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Q: Prove that (x₁, y₁), (x2, y₂), and (x3, Y3) are collinear points if and only if X1 Y1 1 2 Y2 3 y3 1…

A: The given points are:   x1, y1,  x2, y2  and  x3, y3

Q: sin cos 0 cos sin

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Q: 2. Find the limit if it exist of the following: x² - 2x a. (a) lim x2 3x2 10x +8

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Q: A || [3 2 4 2 3 0 2 0 -2 1-3 0 3 2 57 10

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Q: Evaluate lim x−2+ 2x + x x² + x - 2 2x + x→-2- x² + x and lim T X 2

A: limx→-2+2x+2-xx2+x-2 -2+ means just after -2 like x=-1.99999…

Q: A single-lane street 10 ft wide goes through a semicircular tunnel with radius 9 ft. How high is the…

A: Given:The single-lane street is 10 ft wide.The radius of the semicircular tunnel, r=9 ft.We need to…

Q: 3. x²-3 2 x² + x ૨૨ IV 1

A: Please see the below picture for detailed solution.

Q: 5. S sin(3 ln x) X dx

A: Need to find out the integration.

Q: 2. (1 + 3/2x − 1)² = 3 + √3/2x − 1

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Q: Q19

A: Concept Used:  Hyperbola formula:(y-k)2a2-(x-h)2b2=1 The variable h represents the x-offset from the…

Q: You are given the following function. f(b) = b + √b (a) Find the derivative of the function using…

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Q: 2. Use the different differentiation rules and formulas to determine the derivative of the following…

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Q: Part 1: Directions: Complete the table below. EQUATION CENTER 1. C(0,0) 6. 4. x² + y² = 64 x² + y² -…

A: Concept: A circle is a collection of all points in a plane that are uniformly distanced from a fixed…

Q: Q4/ A. Solve the set of equations by using matrix method (2x₁ - 3x₂ + 8x₂ = 6), (x₂ + 7x₂=-4),…

A: A detailed solution is given below.

Q: 2. A circular walkway is to be built around a monument, with the monument as the center. The…

A: The equation of the circle with the centre   ( h, k) and radius r is given by      (x - h)2 + (y -…

Q: Match each of the following with the correct statement. C stands for Convergent, D stands for…

A: Concept used: Divergence: When the values goes to -∞ or goes to ∞ that is it does not approach one…

Q: Find y" for 18 = 4x² +9y² and simplify.

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Q: 2-L-¹ [ 6 2S-8 - 3-2S 95²-16 + 8+6S 4 S²+9

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Q: Find a value of h for which y 3.0 2.5 2.0 1.5 1.0- 0.5 0.5 ƒ(2 + h) − ƒ(2) h 1.0 1.5 = 0. f(x) 2.0…

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Q: The given table represents a pattern of exponential growth.   x      1        2          3 h(x)…

A: Topic- Exponential growth model  we are given points of a exponential function as h(1)=11.8…

Q: Q2/ A: Find the Fourier Series of the function : f(x) = X + n if - < X < π and f(x+2n) = f(x)

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Q: Given that f(x) = 2x + 5 and g(x)= x² + 5, find: a) f(g(2))- b) g(f(2))- c) f(f(2))- d) g(g(2))-

A: We need to find composite function.

Q: 3. Given the function f(x) = (x²-1)/(x-1), determine if the function is continuous or not for all…

A: I am attaching image so that you understand each and every step.

Q: lim √2x² - 4x Evaluate *→

A: The given limit is: limx→2-2x2-4x

Q: Evaluate lim x-2+ 2x + [2x] x² + x - 2 2x + [2x] 2 x² + x - 2 and lim x

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Q: 6. f10e* √1+2e¹dx

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Q: Exercise 3 nd the order of the following differential equations: a.) y" - 2(y")² = (y'-2y)³ d²y V…

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Q: 5. Use derivative rules to find the derivative of h(x) = 3f(x) - 2g(x) - x² f(x) + Show steps for…

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Q: 2y + [[ 2-y]] lim Y>-2- y² +Y-2 lim Y→-2+ 2y + [[2-y]] y² +y-2

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Q: Multivariate Calculus

A: We have to find the region bounded by the curves:x+y=2 ,  x=0 , y=0.Here x+y=2⇒y=2-x⇒y=(2-x)2…

Q: By differentation rules, evaluate the derivative of this and simplify as possible.

A: Given, y=x2+42x

Q: Evaluate_lim_ (√9x² − 5x +1+3″

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Q: 5. A culture contains some bacteria, with the population increasing exponentially. The culture…

A: Let's find bacteria function.

Q: Given that f(x) = (x-7)2 and g(x) = 7 - 4x, find: a) (f + g)(-3)- b) (f-g)(-3)- c) (fg)(-3)- d)…

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Q: 3. Consider f(x) defined as follows: f(x) = 5x² + 13x + 6 |x + 2| [4 - 3x] + x, " x-2 Determine if…

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Q: Check the fundamental theorem for gradients using the function T = 5sz (2+ sin²4) Pick as your path…

A: The given scalar valued function is Ts,ϕ, z=5sz2+sin2 ϕ. According to the Fundamental Theorem for…

Q: 1

A: Given At=te-kt

Q: Find the slope of the graph of the equation at the given point. (If an answer is undefined, enter…

A: Our Aim is to find the slope of the graph of the equation xy-3y2=8-(i) at the given point (14,4)

Q: (y) over any 173. 3/2 =(x² + 2)² y= from x = 0 to x = 1

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Q: (1-x)y' = y²

A: Given Differential equation (1-x)y'=y² This can be written: (1-x)dy=y^2dx; separating the variables:…

Q: Q5/ A: Solve the following differential equation by Laplace : dy - 4y = 16 t =-6, y(0) = 3 dx² dy dx

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Q: For the function f whose graph is given, state the following. (If the limit is infinite, enter 'co'…

A: This question can be solved by using the concept of graphical interpretation of limits

Q: Fill in the blank for the following statements (choose FIVE only) 1- The rectangular…

A: all six are solved

Q: B: Evaluate the following: 2- 6r (5.66) 5r (0.66)

A: Γ(5.66)=67.905 Γ(0.66)=1.366

Q: A mummy was recently discovered. It now contains 66.7% of its original Carbon 14. About how old is…

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Q: t) Identify the type of quadric surface defined by the equation 9y²- and find all x-, y-, and…

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Q: (-4-x)²+2 if x # -5 Let f(x) = 2x + 12 if x = -5 Calculate the following limits. Enter "DNE" if the…

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Q: If x(t) denote the position of a body at time, then the velocity of the body at time t is dt True…

A: Topic = Derivative Correct option =True

Q: dz dt If (z=x. y), where x = cos (t) and y = sin (t) Q3. Use the chain rule method to find

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