Determine an equation of the line tangent to the curve Y = 10 at the point with x- coordinate 1. Ox-10y-20 = 0 -x+ 10y+ 20 = 0 10x +y- 20 = 0 10x-y+ 20 0

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A: Given query is to find the velocity function and the distance traveled.

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A: First I have used  a substitution and made integral easy and then solved it.This is the process.

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Q: 1(10,15) 2. An ant farm population is growing at a rate of g()=15e and declining at a rate of…

A: The rate of growth of an ant farm is gt=15e5t and  the rate of decline of the ant farm is dt=15e5t.

Q: 10 9. Consider the function f(x) %3D Let F(r) be the antiderivative of f(z) with F(1) 0. Then F(x)

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A: Here we have to solve the given problem.

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A: Given function  f(x)= ( 100x5 + sin(-7x))-15

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A: The given integral,                        ∫05ti+t2jdt

Q: 2 2 of

A: Please see the answer below.

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A: According to the guidelines, I am answering first question. Please repost the remaining. Explanation…

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A: Since there are multiple question the first question is answered as per our guidelines. Kindly…

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Q: ||r(t) × r"(t)|| ||r"(t)||³ Use the formula k(t) = to find k(t). r(t) = eti+ej

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A: The detailed solution is given below Thank you

Q: Find the area enclosed by the curves y = y = 2 1- 9x2 2n B 3 D 6. [+

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Q: A. Solve the following problems using the concepts of Parametric Equations. Show complete solutions.…

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Q: d²y 2. Find the second derivative, dx2 a. x = t2 + 1 and y = t3 t2 + 2 and y = sin(t + 1) b. x = | 2

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Q: ||r'(t) × r"(t)|| ||r'(t)||³ Use the formula k(t) = to find «(t). r(t) = e""i+ e'j K(t) =

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Q: 3 Ay 10- Find equation of tangent line at the point (0, 7) for Cos (7x - y)

A: Solving

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A: Dear learner, As per our guidelines we can provide the solution for first one only. Kindly post…

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Q: f(x)=x-4/x^2+2x+17 What monomial expression best estimates the behavior of x-4 as x→± ∞ ?…

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Q: Find the arc length L of the graph of r(t). r(t)= 4 cos(t)i + 4 sin(t)j + tk, 0 ≤ t ≤ 2π

A: The formula for the arc length is given by: L=∫02π(x'(t))2+(y'(t))2dt Here,…

Q: dy Q4) Find for the following functions dx 1. y = 2x + e2x-1 2. y = sec x tan x 3. y = t² + 2t t =…

A: Given

Q: Determine the value of 3A+5B if 10x2 + 25x +5 A Cx +B (x – 1)(x + 1)² (x+1)² 1 - |

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Q: Use Chain Rule to find given w = ds x2 – 2y + z2 and a = cos (st), y = -2s In t and z = s – - VE.

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Q: Calculate the derivative (implicit derivative): y + 19xy = Cos(7x³ - 5y) |

A: topic - implicit differentiation

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Q: Q2) Find the integral value for the following functions dx 4. S x2Vx2-1 ecos-1x 5. S dx V1-x2 6. Se…

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Q: e consider the non-homogeneous problem y" +4y =-32(3x + 2) First we consider the homogeneous problem…

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Q: 3. Sx Vx? – 4dx 4. S(2 – sin 4r) dr 5. S cos x sin? x dx

A: LetI=∫xx2-43dxPut x2-4=udifferentiate 2xdx=duxdx=du2I=∫xx2-43dx.I=∫u32duTake the constant out:…

Q: A. Identify if the given limit is NORMAL, OSL-RIGHT, OSL-LEFT or DNE. x-2 1. lim x-4x2-2x x+4 2. lim…

A: 1)limx→-4 x-2x2-2x x -4.1 -4.01 -4.001 -4.0001 -4 -3.9999 -3.999 -3.99 -3.9 f(x) -0.2439024…

Q: The discontinuities of the function f(x) = %3D 4х-9 are: х2—2х-15 Select one: O 5,3 O -5, -3 -5,3 O…

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