2. An object's position is given by r(t) = < In t2, 5t2 - 2t, cos at >. Find it's velocity, speed and acceleration at t = 1.

Q: 1. Differentiate G(x) = Ax+Bx+C 2. At what point on the curve y= 1 + 3e* – 3x is the tangent line…

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Q: A particle moves on a vertical line so that its coordinate at time t is y = t – 12t + 3, t 2 0,…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: e 1 Determine the equation of the tangent line y=x=2( at x

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Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.…

A: " Since you have posted a multiple questions, we will solve first question for you. To get remaining…

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point C.0. y =1- ... A…

A: Given; ey+cosx=1 at point (π/2,0).

Q: Differentiate

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A: Given: Velocity: vt=-t2i+2t2j+t2k. Then, v't=-2t i+4t j+2t k Find the normal component of the…

Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: 1) Find -(d(PE))/dx in order to find the force acting on the object. (from the equation PE=(1/2)k^2)…

A: Given:

Q: The equation of the tangent line to the curve y = 1 at the point (3,-) is Vx +1 A. x+16y +11=0 B. x+…

A: Please refer the attached solution. None of the option is correct here . I have solved it…

Q: 7) What is the equation of the tangent line of f(x) = xe"+ 3, at x = 0 a) Y= x+3 b) Y= 3 c) Y=…

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Q: If the position of an object is s(t) = 16 + 10.5t – 4.9t meters from zero in t seconds, then what is…

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Q: 17. The equation of the tangent line to the curve y = at the point (3, ÷) is 2 A. x+16y+11= 0 B.…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: A particle moves along the x-axis with velocity given by v(t) = ; sin (t) for time t > 0. If the…

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Q: Suppose that a particle moving along the x-axis encounters a resisting force that results in an…

A: Definition used -                   v=∫adts=∫vdt

Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

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Q: Show that the displacement after time t for motion in a straight line with constant acceleration a,…

A: Given Data: The constant acceleration is: a The initial velocity is: v0 The initial displacement is:…

Q: 3. Find an equation of the tangent line to the curve at the point corresponding to the given value…

A: it is given that; x=et   ; y=ln(t+1) at t=2 at t=2 ⇒x=e2 and y=ln(2+1)=ln3

Q: Find the differential d4y of the function y=x4.

A: Given function is

Q: A. If r = r(t) represents the position function at time t of a certain particle, then what do you…

A: first derivative of position gives- velocity

Q: If s = f(t) denotes the position of a particle at time t, the derivative f'(c) is the of the…

A: Solution:Given      If s=f(t) denotes the position of a particle at time t, the derivative f'(c) is…

Q: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 15. Find the equation of the tangent line to the curve at point (0, In 2). y = In(e' + e4) O 2y + 5x…

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Q: 19. The slope of the tangent to the curve (x2 + y²)² = 4.x²y at the point (1, 1) is 3 3 (a) - () – 1…

A: We have to find slope of the tangent to the curve x2+y22=4x2y at the point 1, 1. We know slope of…

Q: True or False The velocity of a particle whose position at time t is s(t) is the derivative s′(t).

A: Our Aim is to tell whether the statement the velocity of a particle whoseposition at time t is s(t)…

Q: b) The mass (in kg) of a product from a chemical reaction is denoted by 'y'. The dy rate at which…

A: b Separate the terms of both the variables Then let 1+y2=z2ydy=dzand 1+t2=u22tdt=2udu

Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

Q: 9. The velocity, in kilometers per hour, of a car as it beings to slow down is given by the equation…

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Q: Determine an equation of the tangent line to y = (e +2)ª at the point (0, 81), then solve it for y.…

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Q: Find the differential dy of the given function. y = sec2x/(x2 + 1)

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Q: 6) Find dy , where is defined as a function of implicitly by the equation below. dx y + 2x²y³ = 1

A: Given function, y3+2x2y5=1

Q: 1. The position of a particle at time t is given by s(t) = t³ – t2. Using a table, estimate the…

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Q: A particle moves along the x-axis with velocity given by v(t) = 10t + 12 for time t> 0. If the…

A: Given: The velocity of the particle along x-axis is vt=10t+12 The particle is at the position x=2 at…

Q: Find the equation of the two lines that are tangent to the curve x 2 + 4y 2 − 4x − 8y + 3 = 0 at…

A: Given

Q: 6. Find where the velocity of a particle is zero if its position function is x(t)= t In t

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Q: If s(t) is the position on the x-axis of a particle at time t, then the quantitys(t + h)−s(t) / h…

A: If s(t) is the position on the x-axis of a particle at time t,

Q: Express x = ln(7t), y = 9-t in the form y = f(x) by eliminating the parameter.

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Q: To use differentials to approximate V8. You would use x = and dx

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Q: (a) Find the slope of the line tangent to the curve y = sin x at the point where x = T/3. (b) Show…

A: (a) we have to  find the slope of the tangent line to the curve y=sin5x at the point where x=π3. as…

Q: ydx -( x+***ty? dy = 0

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Q: Q 10 Show that for motion in a straight line with constant acceleration a, initial velocity vo , and…

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Q: Q2: If a body is moving along the coordinate line with velocity of: v(t) = sin(nt) 1-The position of…

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Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Wr have to find the derivative of the given function first.

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: If the velocity function v(t) of an object is at its maximum, then the value of a(t), its…

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Q: me Determine the equation of t e 00 te tragen ܘܪܐܐܝ tangent line to y 3- 22+1 at 2:

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Q: 3. Find the equation of the tangent line to the curve at (1,2) * y = 5 - x O A. x-6y + 22 = 0 O B.…

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Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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Q: A car drives down a road in such a way that its velocity (in m/s) at time t (seconds) is v(t) =…

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