For #45, did anyone get the 3rd part of the piece wise function??
I got the other two, but im confused on the 3rd.
You know that you have the restriction of [1,3) (due to the fact that there is an open circle on three it means its not included in the domain) so then you have to just take the slope between the two points given 1,1 and 3,0 and then implement the slope into either point slope form or slope intercept form.
That gives you the equation and the restriction for part three
Hey! that was my question!
and lol Andrew. OH WELL
For 57, how do you find the range? Do you just plug in 0 for x since there is an asymptote there?
Hey Dan, thats what I did and I got the right answer but I'm not completely sure. Also does anyone know how to do 65 parts b,c,d?
You take the circumfrance (8pi-x) and set it equal to the circumrance equation 2pir and solve for r. For c, you set up the pythag. theorum using r and h (height). h^2 + r^2 = 4^2 We know what r is in terms of x, so we plug the answer to be into r^2 and solve for h. Then, for d, use the equation volume = (1/3)pir^2h. Plug in the answer from b for r and the answer from c for h and simplify.
*answer for b
OHHHHH, that makes a lot of sense now. So basically its just a bunch of substitution! Thanks bro
so i'm confused do we do lesson 1.3 tonight? or do we just study for the quiz tomorrow?
Nope, all we have to do is study for the quiz! It'll be on lesson 1.1 and 1.2
For the packet, how do you graph the last one? It has three variables, so what do you do with the a^2 part?
i had the same question.
Im not sure exactly but i think the graph is a semi circle.
what are the domain and range of a tangent(x) graph and secant(x) graphs?
I am also having trouble with those graphs. I have all but those. So if anyone could help with that or I can help with any others.
Which question's graphs question 4 or 5?
I think the tangent(x) graph is a domain of - inf., inf and the range was -1,1 ..But I'm not sure. When I tried to graph the seacant(x) graph it was a straight line at y=1, So I think I got that one wrong too. Anyone else have that? And does anyone know the domain/range of the y=log2x graph?
Oh my gosh, just kidding, I hadn't switched to degrees mode. I got tan to be d: (-inf, inf)r: (-inf,inf) and sec to be d: (-inf, inf) R: (-inf, -1) U (1, inf)
For 1.3 number 22,
did anyone fine the ratio??
i didn't get what they wanted me to do.
Does anybody know how to solve number 42 in section 5?
Did anyone understand 5 & 6 in 1.6 pg 48 ? I saw the answer on the webpage, but can't figure out how to find it?
Okay so for inverses, I know you switch x and y but i'm stuck on what you do afterwards. help!
All you do afterwards is solve for y to get y by itself!
Same with me Brianne, like in #9 in 1.5 we started in class, but then we never totally finished. The last thing I have written down after changing the x and y was x-6 = y(y^2-4) after getting the x and y on seperate sides...
Emily, I think she told us in class that there is no inverse for number 9. If you look at the graph it doesn't pass the vertical line test. Also, i checked the answer and it says the answer is no
Can't you also graph the line and do the horizontal line test to see if it has an inverse too? Or is that something completely different...
*horizontal line test! sorrry :)
OH YEAH! I forgot, thanks! Well that's a relief.
Yeah vertical line test is to make sure it's a function
OH! hey guys do the chapter review problems too because it just chunks everything together which helps alot
Does anyone know how to solve #25 from section 1.6?
Also, for 11-16 for 1.6, the amplitude is from bottom to top right? Not just axis to top/bottom?
I think you just do tangent inverse of 2.5 = X
Oh wait just kidding... plug in tan x into y1 and 2.5 into y2 and graph them. then see where intersect... it should be the first two points to the right of the origin
OHH rightt! that makes sense, thanks!
anyone remember how to get the function of a graph in your Y=? i remember that you need to go to stat, select the 8th one, and plug in l1,comma, l2, ,but how do you get the Y1?
Sam, you mean for like regression models?
go to vars and then, y-vars and then function and then Y1 then press equals and it will be there.
Do we just send an email to Mrs. Johnson
or do we put it on the blog??
does anybody know how to solve #27 from section 2.1?
Yeah, in fact the problem you're looking at is one similar to our summer homework but that's ok. First what you have to do is factor out an X from the denominator to make it equal to X(2X-1). Then there is a trig rule that states as the lim approaches 0 of sin(X)/X it has to equal one. So using that rule you now have as the lim approaches 0 of 1*(2X-1). So now that you have something manageable just plug in your zero into this new limit and you should get the answer being -1
sorry its actually supposed to be 1/(2X-1) but either way you get the same answer
OH YEAH! I forgot, thanks!
Does anyone know how to do #11? I'm confused b/c they switched the x's to y's...
Btw I know the answer is 0 by plugging in -3, but how would you support it graphically
what i did was that i just graphed it by making the variable in the equation x. I don't know if thats right. but when i graphed it, It support my work.
does anybody know how to get 12 for the answer to #25?
For problems like number 33 (pg 62) what does the "int" mean? I tried looking in the answers and it doesn't really explain much.
It's a special type of function. Go to y= on your calculator, hit math, num, then int ( or 5 on your keypad. Then type in x, then ). You should be graphing int(x). It's like stepping stairs with holes on each side of each step.
Wait soo for number 33, i just have to use the calculator?????
Yeah for all the matching ones I just plugged in the equations
Can someone describe what the sandwhich theorem is?
in #47 of this weekends homework there is an a,b,c and d. for letter c. it says that in the piecewise function O- is negative infinity and i thought it would be -1... does anyone know why?
I thought the limit was undefined, because the the left graph never touches the y axis.
Actually, for # 47 the book said the answer was - infinity. I think because the graph keeps going down to - infinity.
did anyone else get DNE for #9 and 3 for #12 on the 2.2 homework??? i feel like its wrong
nvm i know what i did wrong
Can anyone explain number 39 for 2.2? I'm really confused as to what the book is asking.
Oh, nvm, I figured it out.
I don't know y i keep forgetting this, but can someone remind me how to find a horizontal asymptote?
You use the powers, like you use (N(x)^n) / (D(x)^n) (same power, you compare coeff.) If the power in numerator is less than the denominator, hasy = 0, and if the power in the numerator is larger than the power in the denominator then you look at the graph for the slasy.
Oh yeaa. Thanks a lot!
Does anyone understand 26-30s problems? It says to give a formula for the extended function that is continuous at the indicated point
Yeah! Can anyone explain what 26, 28, & 30 are explaining, I looked in the book and still am having trouble understanding what to do?
For number 26, all I did was simplify the graph. Then I checked the graph to see if it was continuous at that point or not.
Im not sure on 28 or 30 though
* simplify the equation
For numbers 9-17 on the hw i am completely lost on how to find the slope and tangent on a curved line. Did we learn this in class or did she just say do the best we can?
Do we do the first 2.4 or both??
Oh and Honsu, if you go back to page 84-85 i think it explains it. Its not completely clear. but it helps a little.
Just the first one. the directions were a little confusing for me. The Secant line is just like what we did in class but the points on the graph are off.
does anybody understand 9-17 on the homework? i have been looking at the book and i get how to find secant slope but how do you get the tangent slope from there? and where does the equation/coordinate Q(2+h, (2+h)^2) come from? its in example 3 on pg 84
You plug in what x is (it'll say x=__) into f(x+h)-f(x)/h. Simplify and you'll have one h left. Solve the limit as h approaches x (basically plug 0 in for h). That's the slope of the curve. Then, to find the line of the tangent. Take the slope of the curve and plug it into an equation where you plug x (whatever x equals orignally) and y (f(x) in the work you did solving for the slope of the curve), then find b. Make an equation. The normal line is a line with a slope that is the opposite reciprical of the slope of the curve, so, use the slope and plut in x and y.
I just can't figure out how to solve 7 and 8 because there's no equation or 13 b and 14 because I got 1, but the answer's -1, if anyone could help.
*limit as h approaches 0 for my first post haha
alright thanks ryan, that helped alot. i figured out how to do 7 and 8. you have to find the slope at each point (q1, q2...) and use P as y2, x2. for example, on #7 you know the P value on the graph is (20,650) and q1 is about (10, 225) and then you just do: change in y/change in x to find slope. and repeat for each point.
ohhhhh, that makes sense. Thanks!
does anybody know how to solve #37 and #38 from section 2.4?
does anybody know how to do 21 and 31 on tonight's homework? they are related
I'd really appreciate if someone could walk me through the word problems (# 23, 25, 27) I know it's rate of change but confused after that
Oh and Will, i think that for number 21 you just plug in (x-h) for whatever X you have. So you have 1/(x+h)-1 and then -1/(x+h) all over h. When you are diving by something you are basically multiplying by it's reciprocal. so you can multiply the entire thing by 1/h
oh yeah i totally forgot about that.. thanks honsu
Could someone help me with #23-27?
Im not sure exactly what they want me to do.
I think for those problems it wants you to interpret the word problem and use the slope of a curve formula.
How do you find the horizontal asymptotes again? And for the vertical ones, its just whatever is in both the top and bottom of the equation right?
For horizontal Asymptotes, u just look at the powers. IF there are the same powers.
look at the coeeficients. If the numerator is less. its 0. If the denominator is smaller, look at the graph.
and vertical ones are just in the bottom.
ooooo that makes it so much clearer
Mrs. Johnson teaches math at Metea Valley High School in Aurora, IL.
Ap Ab Calculus
H Algebra 2 Trig
H Pre Calculus
Regular Pre Calculus