At what point (x, y) is the function f(x) = 6x - 6 closest to the origin? Enter an exact answer. Provide your answer below:

Q: Let f"(x) = -x (2x+1)(x-4)" A. On which intervals is f concave down? B. Give the x value of…

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Q: The four figures below are graphs of the vector-valued function r(t) = 8 cos ti + 8 sin tj + (t/8)k.…

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Q: x2/3+ y2/3=4 from x =1 to x = 8. Find the arc length of the curve x²

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Q: No calculators. Find the exact length of the curve. 0≤x≤l y=2+2x³/2,

A: Length of the curve  =∫ab 1+f'(x)2 dx .

Q: Find the line integral of the vector field F= over the curve C which is the quarter of the unit…

A: To evaluate the line integral of given vector field over the curve C.

Q: Problem 5 Using Laplace transform, solve y" - 4y + 7y = 0 y(0) = 3, y'(0) = 7

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Q: A tenant dropped a spoon from the top floor of her apartment building and it fell according to the…

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Q: 2) Is A P Q R a right angle triangle P(-5,3) Q(-7,8) R(3, 12) and it. name

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Q: For the function f(x)= (8+2x, if x5) A) use definition of continuity at a number (3- step test) B)…

A: Concept: These are the three requirements for continuity: 1). The equation for the function is x =…

Q: A 10​-footladder is leaning against a vertical wall​ (see figure) when Jack begins pulling the foot…

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Q: Find | 22 x²z ds, where C is the line segment from (0,4,-6) to (2,9,-5)

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Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤ y ≤16, 0≤z≤ with density…

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Q: • f'(x) = x − 2x 2 x¹2x² + 1; ƒ(1) = 5

A: We have given f'(x) and we have to find function f(x)

Q: Compute the integral dx.

A: As we know that ∫xmdx=xm+1m+1+C see below the answer and calculation

Q: Find dy if the curve is described by the equation x³ 4x³y + 3y² +Ske y

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Q: Evaluate [P r(t) = (t, sin(t), cos(t)), 0 ≤ t ≤ F. dr where F = (4z, - 3y, 2x), and C is given by

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Q: find y' at y = f(x) уч x 2 x ² y - =1

A: Given function is :-x2y-y2x=1To differentiate it, use :-ddxu(x)v(x)=u(x)ddxv(x)+v(x)ddxu(x).and…

Q: Let A(t)=15(0.8)^0.2t (in milligrams) be the amount of drug in a patients body at time where t is…

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Q: 1 a. Determine whether the Mean Value Theorem applies to the function f(x) = x + on the interval…

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Q: 1) Simplify the expression for f(x + 1) - f(x) where f(x) = e2x - 1) . ) 0 (2 - 1) b) O (2-1)(2 - 1)…

A: option (b) is correct. see below the calculation

Q: Sketch the plane curve represented by the vector-valued function and give the orientation of the…

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Q: Use logarithmic function to find dy/dx, if y=(x^2+5)^sin (2x)

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Q: • Find f' (-1) for f(x) = (3x + 2)² in each of the following ways: • Create a table of secant slopes…

A: Solution is given below:

Q: Sketch the region enclosed by the curves and find its area. 1 y = 2 √1-25x² Y NOTE: Enter the exact…

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Q: Consider the following functions. f₁(x) = x, f₂(x) = x², f3(x) = 4x2x² g(x) = c₁f₁(x) + c₂f₂(x) +…

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Q: Sketch a graph of the function f that is continuous on (-∞,00) and has the following properties.…

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Q: Q3 Let A(1,0,-1), B(-1,2, 1), and C(1, 2, -2) are the three points in a 3D coordinates system. a)…

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Q: Solve the given differential equation by undetermined coefficients. y" + y = 3x sin(x) y(x) =

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Q: The equation of the plane that passes by P(-1, 2, 1) and that is perpendicular to the line x - 3 1-…

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Q: Find the minimum rate of change of f(x, y) – y³e-² at the point (0. — 2).

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Q: Find the largest interval centered about x = 0 for which the given initial-value problem has a…

A: We have to find the largest interval centered about x = 0 for which the given initial-value problem…

Q: The definite integral is equal to [²3x 3xdx Select one: O none of the others O 3 lò O3 lò xdx +3 lit…

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Q: Find the function F that satisfies the following differential equation and initial conditions.…

A: This question is based on diffrentiation equation and solved using Laplace transform.

Q: Consider the region B under the graph of y= * E[5,7], and above the x-axis. 2² +7 x+5 } Estimate the…

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Q: Q1 Pick a number A number is chosen at random from the whole numbers 1, 2, 3, ..., 25. Work out the…

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Q: a 3. Sketch the graph of +₁ f(₂)=1₁ continous function & $²(2)=0, the point (2,1) is 2 £ is…

A: Let's solve.

Q: (6xy - 3y² + 2y)dx + 2(x − y)dy = 0; when x = 0, y = 2

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Q: Why are 9x^2-81y^2=0 and 9x^2-(z^2/4)=0 hyperbolas that pass through the origin and not lines that…

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Q: If b) [ f(x)dx = = n(x)) = 1 then find f(x). = + = 2 x ² + 6x -tan(x) - 4e + + 6x + C

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Q: . Approximate (1.999) by using linearization.

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Q: Find the relative rate of change. Evaluate the relative rate of change at the given value(s) of t. -…

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Q: Calculate the following antiderivatives: (a) ∫ 8t− 6t^6 −5dt =  +C. (b) ∫ 1/u^7/4 + 3.5 sqrt u du…

A: a) Given:       ∫8t-6t6-5dt  =∫8t dt-∫6t6 dt-∫5 dt taking constant out     =8∫t dt-6∫t6dt-5∫ dt…

Q: x4 dx X³- 2x²-7X-4

A: The given integral is: I=∫x4x3-2x2-7x-4dx   As we know the common integral.…

Q: Find r'(t), r(t0), and r'(t0) for the given value of t0. r(t) = (1 + t)i + t3j,    t0 = 1 r'(t0)  =

A: Given the curve r(t)=1+t i+t3 j, t0=1

Q: 6. The acceleration of the position function s(t) = 4t² - 8t + 2 when t = 7. a) 7 b) 48 c) 142 d) 8

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Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

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Q: ries of f(x) = lor series. =0 =0 =0 (−1)²+1 (-1)²+¹ (-1)". 1 (x-7)" 8n+1 (x (x − 8)¹+1 7" E(-1)", =0…

A: We have to find the Taylor series from the given condition and also indentify  the valid interval

Q: The equation of the plane that passes by P(2, 0, -1) and that is perpendicular to the line x-5 2-y Z…

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Q: Write v as a linear combination of u and w, if possible, where u- (3, 2) and w(2, -1). (Enter your…

A: Given :- u =(3,2) , w=(2,-1),v=(-6,-4)  Write v as linear combination of u and w

Q: Solve 4x - 5 = 19. O A. x= 10 OB. X=6 OC. x= 3.5 OD. x=8

A: We can find the answer as below.