Find the average velocity of the function over the given interval. y= - 3x? - x, [5,6] – X,

Q: The position of an object moving along a line is given by the function s(t)=-9t^2+27t Find the…

A: s(t)=-9t2 + 27tHence, s(1 + h) = - 9  x (1 + h)2 + 27 x (1 + h) = - 9h2 - 18h – 9 + 27 + 27h = - 9h2…

Q: The velocity of a car is recorded at half-second intervals (in feet per second). Use the average of…

A: Given Data: The travelled duration is: Δt=4 s The table is given the figure represent the velocity…

Q: Find the average rate of change of the function over the given interval. f(t) = 13 + cos t a. - T, 2…

A: given f(t)=13+cos(t) To find the average rate of change of f(t)

Q: Use the table to find the instantaneous velocity of y at the specified value of x. /69 18) x 1 O.2 X…

A: Calculation:From the given Table, the value of y at x = 1 is 0.25.Compute the instantaneous velocity…

Q: Show how to make a quick estimate (to two decimal places) of V(4.98)² – (3.03)² without using a…

A: Given we have given  4.982-3.032

Q: a) Find the average velocity for the time peric when t = 2 and lasting (i) 0.5 seconds (ii) 0.1…

A: Since you have asked multiple part question, we will solve the first3 part of the question for you…

Q: The position of a particle at time t is s(t) = t3 + t. Compute the average velocity over the time…

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Q: Find the maximu rate of change of the function f(x y) = x² + xy + y² at the point (6, 7). O 386 V653…

A: →Maximum rate of change of function is along gradient, which is given by,               ∇f(x,y) =…

Q: The position of an object moving along a line is given by the function s(t) = - 17t +136t. Find the…

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Q: Let Y= x² +3 2 d. Find the average rate of Change of Y'o 79 over the following with respect to x…

A: Given query is to find the average rate of change and instantaneous rate of change for  y = x2+3

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

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Q: Find the average rate of change of the function over the given intervals. h(t) = cot t 5π7π а. 4 ' 4…

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Q: Find the curve length of the given functions in the given interval

A: Find dx/dt and dy/dt using product rule.Then find (dx/dt)^2 and (dy/dt)^2.

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: The equation of the normal to the curve f(x) x2 - 5 at x = 2 is (a) y = -1/4(x+2) (b) y =…

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Q: Let f(x) = x + vx . The equation for the tangent line at the point (1, 2) is y = m(x – 1) +2, where…

A: Given: fx=x+x

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: Find the total derivative dy/dw. Y=3x+2w+5z? x=4 In(w-) z=ez+3x

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Q: For function f (x, y) y? x²+1 Find the maximum rate of change of f at the point (1, 2)

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Q: Find the average velocity of the coin over the interval [1,2] : Average velocity is feet per second…

A: Consider the given height function, st=-16t2+155   The average velocity of the coin over [1, 2] will…

Q: Find the total derivative, (w? – 3w) dy of: y = f(x, w) 5x? + 4xw + w?, where r = g(w) --

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Q: The distance of a particle from some fixed point is given by the following function. s(t) =t + 4t-3…

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Q: The position of an object moving along a line is given by the function s(t) = – 6t +30t. Find the…

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Q: If a ball is thrown in the air with a velocity 48 ft/s, its height in feet t seconds later is given…

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Q: Find the equation of the tangent plane to z=e^y+x+x^4+6 at the point (4,0,267).

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Q: Estimate V26 by using linear approximation of f (æ) = V¤ about the value x 27. Round your answer to…

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Q: Find the average rate of change of f(x) = x2 + 3x + 1from 1 to 2. Use this result to find the…

A: Average rate of change of a function f(x) is calculated as the total change in the function divided…

Q: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting at t…

A: Given: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting…

Q: 1a. What is the average velocity of the car between t=0 and t=15?   1b. What is the average…

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Q: Use the Simpson's rule to estimate S, ex dx with n = 4

A: Consider the given integral ∫12ex2dx with n = 4. Simpson's rule is,…

Q: If a baseball is thrown upward with a velocity of 45 m/s, its height in meters t seconds later is…

A: We know that, Average velocity          = change in position/time elapsed.

Q: Find the slope of the tangent line of the function y = In (x) at x = e2 O1/e? 4/et O 1/e* O 2le2

A: Topic = Derivative As per guidelines, At a time only one question can be answered out of different…

Q: The velocity function, in feet per second, is given for a particle moving along a straight line,…

A: The velocity function, in feet per second, is given for a particle moving along a straight line,…

Q: Find the average velocity of the function over the given interval. y =x? + 4x, [2,8] 21 O A. 2 О В.…

A: The average velocity of the function f(x) over the interval [a,b] is given by: f(x)=f(b)-f(a)b-a

Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: What is the equation of the normal line to the curve y = cos æ at the point (6,0) ... A y = -x +; 2…

A: Given:- y = cos(x)  To find:- Equation of normal line on given curve at point (π/2 , 0)

Q: 4) For the function p = x2y+ yz at the point (1,2,-1), find its rate of change with distance in the…

A: Given data: Function:

Q: The velocity of a car is recorded at half-second intervals (in feet per second). Use the average of…

A: Given

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

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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: Consider the following function. f(t) = 4t + 5 Find its average rate of change over the interval [1,…

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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: The position of an object moving vertically along a line is given by the function s(t) = -4.9t + 28t…

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

Q: In r d) y = (V)" at (1, 1)

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Q: f(30+h}-f{30)

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Q: Given the function g(x) = the function over the interval-11SA-1. + 10x + 18, determine the average…

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Q: The position of an object moving along a line is given by the function s(t)=-16t64t. Find the…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: The derivative of y with respect to given a = 1 is Onone of the choices O y = yx³-1 O V = 0 = = 9 *…

A: I have stated the used formula in the solution

Q: Approximate v10 using a linear approximation. Round to 5 decimal places. つ

A: Here is the solution

Q: Find the average speed over the time interval [1, 5] (time in seconds) of a particle whose position…

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