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Homework: HW Section 2.3 Score: 0 of 5 pts2.3.87-GC Assigned MediaDo the following for the function g(x) = 2x+6. (a) Express the slope of the secant line in terms o...

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Homework: HW Section 2.3 Score: 0 of 5 pts2.3.87-GC Assigned MediaDo the following for the function g(x) = 2x+6. (a) Express the slope of the secant line in terms of x and h. (b) Find msec for h =0.5,0.1,and 0.01atx=1 What value does msec approach as h approaches 0? (c) Find the equation for the secant Iine at x = 1 with h = 0.01. Graph g and the secant line found in part (c) on the same viewing window: (a) Type the slope of the secant line in terms of x and h.msec(Simplify your answer )Enter yo

Homework: HW Section 2.3 Score: 0 of 5 pts 2.3.87-GC Assigned Media Do the following for the function g(x) = 2x+6. (a) Express the slope of the secant line in terms of x and h. (b) Find msec for h =0.5,0.1,and 0.01atx=1 What value does msec approach as h approaches 0? (c) Find the equation for the secant Iine at x = 1 with h = 0.01. Graph g and the secant line found in part (c) on the same viewing window: (a) Type the slope of the secant line in terms of x and h. msec (Simplify your answer ) Enter your ansver in tna ansvror DOx and thon click Cneck Answor purts {unatng



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Problems $85-92$ require the following discussion of a secant line. The slope of the secant line containing the two points $(x, f(x))$ and $(x+h, f(x+h))$ on the graph of a function $y=f(x)$ may be given as $m_{\mathrm{sec}}=\frac{f(x+h)-f(x)}{(x+h)-x}=\frac{f(x+h)-f(x)}{h} \quad h \neq 0$ (a) Express the slope of the secant line of each function in terms of $x$ and $h$. Be sure to simplify your answer. (b) Find $m_{\text {sec }}$ for $h=0.5,0.1$, and 0.01 at $x=1 .$ What value does $m_{\text {sec }}$ approach as h approaches $0 ?$ (c) Find an equation for the secant line at $x=1$ with $h=0.01$. (d) Use a graphing utility to graph fand the secant line found in part ( $c$ ) in the same viewing window. f(x)=2 x+5

So what we're given this equation F. Of X equal to two X plus five. And the first thing we're gonna do is um actually right down the slope of the C. Can't line in terms of our F. Of X. And H. So we're told that the slope of the secret line is equal to F. Of X plus H minus F of X divided by H. So now we just have to plug in these values. So in this case F. Of X plus each would be two times X plus each Plus five then -2 x minus five. Since we need to distribute this minus sign. And then we divide everything by H. So if we simplify this we have to X plus two H plus five minus two X minus five divided by H. So this two X. Will cancel out the negative two X. And this fire will cancel out with the negative five. So we're left with two age divided by age which is just equal to two. And now for part B we want to find the slope. Um Given that H. is equal 2.5 0.1 and point oh Oh sorry .01 and we're told that X. Is equal to one so X. Is equal to one and H is equal to 10.5 point one and 10.1 So if we plug this into our um difference equation or R. C. Can't line slope M. C. Can't We have f. of x plus .5 minus F. X divided by H. So let's plug in these values F. Of X plus five is going to be two times. Ex well in this case X we were told is equal to one. So it's gonna be two times one plus 10.5 which is equal to 1.5 um Plus five than minus two times 1 -5 divided by point size. So we get this will cancel this So you get 3 -2 divided by five, It's equal to one divided by five which is equal to two. And now we find this again instead of using H is equal 2.5 we'll let age equal 2.1. So we get two times X which is equal to one plus 10.1 plus five minus two minus five. And we divide by .1. So this is equal to two times one plus 10.1 would be 2.2. And then we can cancel out these five. So we have 2.2 minus two divided by 20.1 Which is then equal 2.2 divided by .1 which is equal to two again. And then the last one that we want to figure out Is when H is equal 2.01. So we have two times one plus .01. Yeah Minour or sorry plus 5 -2 times one minus five Divided by .1. So this is equal to two times one. Plus point to one Will be two 02. And then again these fives cancel out. So we have -2 Divided by .01 which again is equal to two. So all three of our slopes were equal to two, which was what we wanted to find. Since in part a we found that the secret line Slope is equal to two and now for part C we're gonna figure out the equation. Um for the C can't line for X is equal to one and so X is equal to one and H is equal two point oh one. So we already know that the slope of the C. Can't line Is equal to two. So we can set up an equation where Y. Is equal to two times X plus B. And we can plug in this .1 um comma whatever we get when we plug it into our original equation. So if you plugged in 1.5 of X would get two times one plus five which would be seven. So we want to plug in this point One come seven and make sure it's on this line. So let's say seven is equal to two times one plus B. So seven is equal to two and then We can -2 3, 5 is equal to be, so then we have Y. Is equal to two X plus five.


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