Find the average rate of change of h(t) = t3 + 2t² – t – 1 for the domain [0,5].

Q: The atmospheric pressure at altitude h (kilometers) for 11 ≤ h ≤ 25 is approximately…

A: Given: P(h)=128e-0.157h

Q: The population ( in hundreds ) of fish in a pond is given by P(t) = 2t + sin(2t –10) t months from…

A:

Q: 16. F(m, r) = Gm/r² at (100, 10)

A: We wil use rules related to multi variable calculus to solve this.

Q: 9) Where is the function ht) = (t+ 5) differentiable?

A: Given         h(t)= t+51/3

Q: dy For the function dt d'y = 5 cost, the third order derivative is dt3

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Q: Please answers part c, d

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

Q: 3. If f (t) = -t + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A: We are allow to solve only one question at a time  Thank you for your question

Q: |If f(x) = a4 is the parent cubic function, prove that the AVERAGE rate of change of f(x) over the…

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

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Q: Compute the average rate of change of f (t) = 40t – 16t over the indicated intervals. %3D -

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Q: Consider the following function. F(t) = 2t + 5 Find its average rate of change over the interval [1,…

A: f(t)=2t+5 Average rate of change formula is  f(b)-f(a)b-agiven interval is…

Q: Find the Average Rate of Change of the following function (That is, from t = 2 to t = 5.) over the…

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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: Differentiate the function y = e0.4t. dy dt

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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: 5. If f (t) = -3t° + 7t, describes the movement of a whale in meters. What is the average rate of…

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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: The total derivative of the function ƒ(x,y) =x²y at x = 1,y = 2 and dx = - dy = 2 is O a. 20 O b. 21…

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Q: 1. For the function f (t) = t² – 4 over the interval [-1, 3], find a. the net change b. the average…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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

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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>=0 if the position is x =2  at time t = 0  Position…

Q: Find the average rate of change of the function f(t) = 10t? from t = 1 tot= 4. %3D %3D O-20 O 30 O…

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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: ind the average rate of change between the given points f(t)=t^2 -2t between t=2 and t=5

A: f(t)=t2-2tf(2)=4-4=0f(5)=25-10=15average rate of change  =f(5)-f(x)5-2  =15-03  =5

Q: Find the total derivative dz/dt , given z = x2-8xy-y3 , where x= 3t and y= 1–t

A: Suppose z is a function of x and y that is z=fx,y where x and y is the function of t that is x=xt…

Q: Sketch the graph of y = v4-x², - 2<x<2. a

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Q: H.W: Use the chain rule to find the derivative of w= x² + y² with respect to t dw dt with x = cost +…

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Q: Let Q(t) = t^2. As in the previous exercise, find a formula for the average rate of change of Q over…

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Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 4t - 3 mis over…

A: Given velocity of particle is vt=4t-3. To find the dispalcement of particle over time interval 2,5.…

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

A: We have to solve

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the…

A: Given that rate of change of y is proportional to y that is, dydt=ky        ...(1)

Q: The average rate of change of f(x)=mx+b on the interval a,c is: В. 1 С. т А. 0 тс -та + 2b D. E.…

A: Let f(x) be any function.Then, Average rate of change of f(x) over [a,c] = f(c) - f(a)c-a

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: XVII. For w = x³ + xy² +yz, find the rate of change of w at point (1,2,3) in the direction towards…

A:

Q: H.W: Use the chain rule to find the derivative of w=x² + y² with dw with x cost+ sin t, y= cost-sint…

A: If w is a function of x and y and x,y are functions of t then we get by Chain rule, dw/dt=…

Q: Given the following function, determine the maximum rate of change of it at the point P(0,0, 1/2).…

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Q: The position of a particle at time t is s(t) = 4t^3. Compute the average velocity over the time…

A:

Q: Find the average rate of change of the function over the given interval. f(t) = 4t2 – 1, [1, 1.1]

A: Given data: The expression for the function is f(t)=4t2-1. The given limit of t is [a, b]=[1, 1.1].…

Q: Find the net change and the average rate of change of the function           d(t) = 16t^2  between t…

A: Given D(t)=16t^2 , Between t=1 to t=5

Q: 5. Let f(x, y) = x² - y² x² + y² a. In which direction should you move from the point (1,1) to…

A: Maximum rate of change occurs in the direction of gradient vector of the function.

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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Q: Determine the average velocity of the function f(t) = vt +1 between the time intervals t = 3 and t =…

A: Given that: f(t)=t+1

Q: Suppose h(t) = t² + 11t + 7. Find the instantaneous rate of change of h(t) with respect to t at t =…

A:

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: Determine the average rate of change of the function y= sinx from x= 0 to x=. a) 0 b) 1 O d) 를

A: The average rate of change of a function, g(x) , over the interval, c,d is calculated using the…

Q: Q. Find the rate of change of z = In Vx² + y² at (3, 4, In 5), (a) In the direction of the positive…

A:

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: Find the average rate of change of the function over the given interval. f(t) = 14 + sin t a. 0, T…

A: Given that

Q: The position of a particle at time t is s(t) = 4t^3. compute the average velocity over the time…

A:

Q: Find the third derivative of f (z) = T2x +I. fll! (z) =

A: Explanation of the answer is as follows