Why is it useful to find instantaneous rates of change? Once I find the instantaneous rate...
Why is it useful to find instantaneous rates of change? Once I find the instantaneous rate of change, what can I do with it? If this is too broad, try to choose one example
Homework Answers
Let's take the example of a racing car on a racing track.
Think about what its average velocity is. Velocity, in general, is the rate of change of displacement. Its displacement is zero overall, as it starts from the same place and finishes the lap at that place only. Hence, its average speed is zero. But is this even close to what the velocity of the car was actually?
Obviously not. Its instantaneous speed is around 300kmph! Which is not even close to what its average speed is.
So, instantaneous rates of change are important.
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Why is it useful to find instantaneous rates of change? Once I
find the instantaneous rate...
2. The Derivative. No surprise here. Be able to discuss tangent and secant lines, the difference quotient, instantaneous vs. average rates of change, local linearity and zooming, and how th...
2. The Derivative. No surprise here. Be able to discuss tangent and secant lines, the difference quotient, instantaneous vs. average rates of change, local linearity and zooming, and how they are all related (including the limiting process). Below are a few possible essay questions for the final exam. I can guarantee at least one and possibly up to three questions related to the concepts below will be on the final exam. I suggest that you try writing out essays to...
t Average and Instantaneous Reaction Rates ous Answe An average reaction rate is calculated as the...
t Average and Instantaneous Reaction Rates ous Answe An average reaction rate is calculated as the change in the concentration of reactants or products over a period of time in the course of the reaction. An instantaneous reaction rate is the rate at a particular moment in the reaction and is usually determined graphically Correct Part C The reaction of compound A formi studied and the following data were collected ng compound B was What is the instantaneous rate of...
To find the instantaneous rate of change at x=3 Using the definition f(x +Ax) -...
To find
the instantaneous rate of change at x=3
Using the definition f(x +Ax) - f(x) Slope T - lim Ar-0 To find the instantaneous rate of change at x 3
Find instantaneous rate of change for t(x)=3sinx +3, x=a Find Average rate of change for t(x)=3sinx...
Find instantaneous rate of change for t(x)=3sinx +3, x=a Find Average rate of change for t(x)=3sinx +3, [a,b] for any value of a and b
15. Find the instantaneous rate of change of f(x) = 4x - 2 at x =...
15. Find the instantaneous rate of change of f(x) = 4x - 2 at x = 5 16. Find the slone of the tangent lino to 2
B. find the instantaneous rate of change for the demand for boxes of nails C. at a price of $3 per box, at what rate doe...
B.
find the instantaneous rate of change for the demand for boxes of
nails
C. at a price of $3 per box, at what rate does demand
change
3. Customer demand for N boxes of nails at p dollars per box, as given by N(p) = 80 - 3 p? 15 p 5 5 Find the average rate of change of demand for a change in price from $2 to $4. (3 pts.)
9. What is the instantaneous rate of change of 2 = f(x,y) = x + xy...
9. What is the instantaneous rate of change of 2 = f(x,y) = x + xy (with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2) ? e) none of these V13 12 -8 V13 13
Consider the following function. f(t)4t5 Find its average rate of change over the interval [1, 4] At Compare t...
Consider the following function. f(t)4t5 Find its average rate of change over the interval [1, 4] At Compare this rate with the instantaneous rates of change at the endpoints of the interval f(4) Need Help? Read It Watch It Talk to a Tutor Consider the following function f(x)x18x 2 Find its average rate of change over the interval [-9, 1]. Ay Ax Compare this rate with the instantaneous rates of change at the endpoints of the interval f-9) f(1) Need...
What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal...
What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2)? -8 -3 4 12 b) c) d) e) none of these 113 113 V13 113 a) o What is the average rate of change of z = f(x, y) = x² + xy(with respect to horizontal distance) as one travels from (2,1) to (4,-2)? 2 5 12 c) d) e) none of...
P(x) = x2-2x-15, find the instantaneous rate of change at x = 2. 7, For the function a. -15 b. 3 c. d. 0 None of th...
P(x) = x2-2x-15, find the instantaneous rate of change at x = 2. 7, For the function a. -15 b. 3 c. d. 0 None of the above e. If the total revenue function for a blender is 8. R(x) = 36x-0.0 1x2 where x is the number of blenders sold, what is the average rate of change in total revenue Rix) as x increases from 10 to 20 blenders? a. $34.00 b. $356 c. $35.70 d. $35.50 None of...
2. The Derivative. No surprise here. Be able to discuss tangent and secant lines, the difference quotient, instantaneous vs. average rates of change, local linearity and zooming, and how they are all related (including the limiting process). Below are a few possible essay questions for the final exam. I can guarantee at least one and possibly up to three questions related to the concepts below will be on the final exam. I suggest that you try writing out essays to...
t Average and Instantaneous Reaction Rates ous Answe An average reaction rate is calculated as the change in the concentration of reactants or products over a period of time in the course of the reaction. An instantaneous reaction rate is the rate at a particular moment in the reaction and is usually determined graphically Correct Part C The reaction of compound A formi studied and the following data were collected ng compound B was What is the instantaneous rate of...
To find
the instantaneous rate of change at x=3
Using the definition f(x +Ax) - f(x) Slope T - lim Ar-0 To find the instantaneous rate of change at x 3
15. Find the instantaneous rate of change of f(x) = 4x - 2 at x = 5 16. Find the slone of the tangent lino to 2
B.
find the instantaneous rate of change for the demand for boxes of
nails
C. at a price of $3 per box, at what rate does demand
change
3. Customer demand for N boxes of nails at p dollars per box, as given by N(p) = 80 - 3 p? 15 p 5 5 Find the average rate of change of demand for a change in price from $2 to $4. (3 pts.)
9. What is the instantaneous rate of change of 2 = f(x,y) = x + xy (with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2) ? e) none of these V13 12 -8 V13 13
Consider the following function. f(t)4t5 Find its average rate of change over the interval [1, 4] At Compare this rate with the instantaneous rates of change at the endpoints of the interval f(4) Need Help? Read It Watch It Talk to a Tutor Consider the following function f(x)x18x 2 Find its average rate of change over the interval [-9, 1]. Ay Ax Compare this rate with the instantaneous rates of change at the endpoints of the interval f-9) f(1) Need...
What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2)? -8 -3 4 12 b) c) d) e) none of these 113 113 V13 113 a) o What is the average rate of change of z = f(x, y) = x² + xy(with respect to horizontal distance) as one travels from (2,1) to (4,-2)? 2 5 12 c) d) e) none of...
P(x) = x2-2x-15, find the instantaneous rate of change at x = 2. 7, For the function a. -15 b. 3 c. d. 0 None of the above e. If the total revenue function for a blender is 8. R(x) = 36x-0.0 1x2 where x is the number of blenders sold, what is the average rate of change in total revenue Rix) as x increases from 10 to 20 blenders? a. $34.00 b. $356 c. $35.70 d. $35.50 None of...
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