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Carissa15
 one year ago
Please help. I have a calculus question about the secant of a parabola y=x^2 that passes through points A=(2,4) and A'=(2+delta x, 4+ delta y) , find the slope of this secant. I am then given a) delta x =0.01 and b) delta x = E. To answer this do I just sub in the a) and b) values of x and solve the equation?
Carissa15
 one year ago
Please help. I have a calculus question about the secant of a parabola y=x^2 that passes through points A=(2,4) and A'=(2+delta x, 4+ delta y) , find the slope of this secant. I am then given a) delta x =0.01 and b) delta x = E. To answer this do I just sub in the a) and b) values of x and solve the equation?

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: the slope m of your secan t, is: \[m = \frac{{{\delta _y}}}{{{\delta _x}}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1furthermore, we can write this: \[\Large 4 + {\delta _y} = {\left( {2 + {\delta _x}} \right)^2}\]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1you then solve for delta y? As values for delta x are already given?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1from my last equation, we have: \[\Large 4 + {\delta _y} = 4 + {\left( {{\delta _x}} \right)^2} + 4{\delta _x}\] so we can simplify as below: \[\Large \frac{{{\delta _y}}}{{{\delta _x}}} = {\delta _x} + 4\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1438251569667:dw

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1yes, that makes sense. I do not understand how the two parts of a) delta x=0.01 and b) delta x=E come into this? Sorry, probably very silly question, does not get covered in my textbook and getting confused.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1delta x= E means delta x= infinity?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think taht we have to substitute: \[\Large \begin{gathered} {\delta _x} = 0, \hfill \\ {\delta _x} = \varepsilon \hfill \\ \end{gathered} \] into the formula above

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2I think you want to finish part \(a\) first let \(\delta_x=0.01\) and find the slope of secant

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1oops..: \[\Large \begin{gathered} {\delta _x} = 0.01, \hfill \\ {\delta _x} = \varepsilon \hfill \\ \end{gathered} \]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1Great, once the formula is broken down. I have now substituted delta x=0.01 and found delta y is =0.0401. Will do the same with Epsilon (except won't get a numerical value)

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1knew what you meant :)

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1\[4+\delta y=4+(\delta x)^2+4 \delta x\] then subtracted 4 on both sides to isolate \[\delta y\]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1then got \[( \delta x)^2+4 \delta x\] then sub in my x value for a)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2For part \(a\), below works too : \[m= \dfrac{y_2y_1}{x_2x_1}=\dfrac{(2+0.01)^22^2}{0.01}\]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1am i correct in thinking that with epsilon I will not be able to find a value, I will just be left with an equation after substitution?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1438252734043:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, plugin \(\delta_x = \epsilon\) and simplify the secant expression as much as you can

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1great, thank you so much. So much clearer now :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2np, for part \(b\) i think you should get : \[m= \dfrac{y_2y_1}{x_2x_1}=\dfrac{(2+\epsilon)^22^2}{\epsilon} = \dfrac{4\epsilon +\epsilon^2}{\epsilon} = 4+\epsilon\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Looks your teacher wants you see how a secant line approaches to tangent line by decreasing the value of \(\epsilon\)

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1As simplified as I can? is that what you mean?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, but I have simplified that for you already

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1when using \[ \frac{ \delta y }{ \delta x }\] I get a different result than y2y1/x2x1

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2both should give you same answer, show me ur work

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1\[\delta y = (\delta x)^2+4 \delta x\] then after substitution i get \[\delta y = (0.01)^2+4(0.01) = 0.0001+0.04 = 0.0401\]

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1and with \[\frac{ y2 y1}{ x2x1 }=\frac{ (2+0.01)^22^2}{ 0.01 } =4.01\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2looks fine, whats wrong with that ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2notice that slope of secant equals \(\dfrac{\delta y}{\delta x}\), not just \(\delta y\)

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1ok, so my first one i still need to divide by delta x. then they will be the same. :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yep! Easy, slope = (change in y)/(change in x)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2thats the highschool definition of slope, and it still works! :)

Carissa15
 one year ago
Best ResponseYou've already chosen the best response.1Awesome, thank you so much. Lifesaver!

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Here is a little animation that shows how the secant line approaches/diverges from tangent line as \(\delta_x\) is decreased/increased dw:1438254466089:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\(A\) is a fixed point. Notice that as the point \(A'\) approaches the point \(A\), the secant line approaches the tangent line.
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