The position of a moving particle is given by s(t) = t2 – 2t + 6 on the interval 0

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

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Q: The position of a moving particle is given by s(t) = t2 – 7t + 4 on the interval 0 <t< 4, where 's'…

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Q: For the position function, s(t)=-16t2+103t​, complete the following table with the appropriate…

A: Consider the position function, s(t) = 16t2+103t.

Q: The velocity in m&gt;s of an object moving alonga line over the time interval [0, 6] is v(t) = t2 +…

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Q: Answer part D.

A: As we consider the approximation of function have already done in  above parts,(D) When change in x…

Q: Please answers part c, d

A: As per norms, the first three questions are answered. The questions concern the linear approximation…

Q: Given y = V4x + 5, find the differential dy when a = 7 and dæ = 0.3. %3| Round your answer to three…

A: Given data:   The expression for the given function is y=(4x+5)1/2. The given value of x is x=7. The…

Q: Evaluate the derivative of the function r(t)=⟨lnt,3t+1,t2⟩ at t=1.

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Q: suppose y = √(3x + 1), where x and y are both functions of t. If dx/dt = 2, find dy/dt when x=5

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Q: The position of a moving particle is given by s(t) = 2t2 – 18t on 2 <t< 9 where 's' is in meters and…

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Q: The acceleration function of a particle moving along a line is given by: a(t) = 4t – 2 in m/s² and…

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Q: The position of a particle at time t (s) is s(t) = t2 + 1 m. Compute its average velocity over [2,…

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Q: Use the Product Rule to compute the derivative: d. Find dt (e + 1)(t + 9)) at t = 13

A: Topic :- Derivative

Q: b) Use the velocity function v(t) = 2e" to compute the distance traveled by an object over the time…

A: The detailed solution is given below  Thank you

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: The acceleration function of a particle moving along a line is given by: a ( t ) = 2 t + 3 in m / s…

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Q: Because a new employee must learn an assigned task, production will increase with time. Suppose that…

A: To find the number of units completed in t hours by the new employee, integrate the rate of…

Q: Let v(t) = -13t + t² be the velocity, in ft/sec, of an object at time t, in seconds. a) What is the…

A: Given velocity function, v(t)= -13t + t²

Q: Find the antiderivative of the given derivative. ds = 5t(212 – 1)3 dt

A: Solution:-  given that  dsdt=5t(2t2-1)3 now  using identity (a-b)3=a3-b3-3ab(a-b)

Q: Use the Quotient Rule to compute the following: t2 +1 d at t = 2 dt t2 The derivative is:

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Q: Let y = f(x), where f(x) = 6x2 + 3. Find the differential of the function. dy =

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Q: The position of a particle at time tis s(t) = 2t 3• Compute the average velocity over the time…

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Q: A moving object has a constant acceleration of -9.8 meters per square second. If its initial…

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Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 3t2 – 60t.…

A: v(t)=3t2-60t,    t≥0the particle is moving to the right whenv(t)&gt;03t2-60t&gt;03t(t-20)&gt;0

Q: A particle moves along the x-axis with velocity given by v(t) = 6t – 6t for time t > 0. If the…

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Q: A particle moving along a line has position s(t) = t 4 - 18t2 m at time t seconds. At which times…

A: st=t4-18t2 Substitute 0 for s(t) into above position function. st=0t4-18t2=0t2t2-18=0t=0 or t2=18t=0…

Q: The position of a moving particle is given by s(t) = t2 – 7t + 5 on the interval 0 <t< 5, %3D -…

A: First I have find the Instantaneous velocity and then Average velocity then making them equal and…

Q: Show that for an object falling according to Galileo’s formula, the average velocity over any time…

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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: For the given velocity  v(t) = 10t +12 for t&gt;=0 if the position is x =2  at time t = 0  Position…

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s^2 is…

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Q: What is the derivative of this integral?

A: We know that

Q: Q2) A: Compute at the point (1, 0) for the function dx S(x,y) = cot 1(4x + em(sin2xy)) + sinh(3) +…

A: Given that, f(x,y)=cot-14x+elnsin 2xy+sin h(3)+log2x2 Which can be re - written as,…

Q: Find the maximum rate of change of f(s,t)=te^(st) at the point (0,−5).

A: We have to solve

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: A particle moves along the x-axis with velocity given by v(t) = 6t2 – 18 for time t > 0. If the…

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Q: Assume that x and y are both differentiable functions of t and are related to the equation: y =…

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Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: Let y = f(x), where   f(x) = 4x2 + 6.   Find the differential of the function.   dy =?

A: Given: y=fx=4x2+6 now differentiating given function with respect to x

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 1 for time t > 0. If the…

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Q: A train moves at a velocity of v(t)= 3t" - 3200t km/sec where t in seconds is the time passed since…

A: Find your answer below

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² – 10t for time t> 0. If the…

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Q: A particle is moving in a straight line with the velocity v(t) =1-t,0<t< 3. Compute the distance…

A: We have V=1-t⇒dxdt=1-t∫0△xdx=∫(1-t)dt

Q: Suppose y = (sq. root of) 2x + 1, where x and y are functions of t. (a) If dx/dt = 9, find dy/dt…

A: y=2x+1 Differentiating with respect to t, we get dydt=122x+1·d2x+1dt…

Q: A particle initially situated at the origin moves along the x-axis so that its acceleration at any…

A: Integrate the expression a(t)=2t-7 to find the velocity of the particle.…

Q: A particle moving along a line has position s(t) = t4 − 18t2 m at time t seconds. At which times…

A: St=t4-18t2The particle passes through the origin when St=0t4-18t2=0t2t2-18=0t2=0   t2-18=0⇒t=0…

Q: Suppose that a change in biomass B(t) at time t during the interval [0,5] follows the dB equation…

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Q: The position of a moving particle is given by s(t) =t - 3t + 6 on the interval 0<t<6, where 's' is…

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