2. Given the surface: f ( x, y ) = (e^ x + y) + ln( y^ 2 + x) a. Show that the point (0,1) is located on the curve f ( x, y ) = e , and find the equation of the tangent line to the curve, at that point. b. Find the slope of the tangent line to the curve, that results from the intercept of the plane x = 0 with the surface, at the point where y = 1 . c. Find the slope of the tangent line to the curve, that results from the intercept of the plane y = 1 with the surface, at the point where x = 0 . how to solve this kind of questions? explanation will be very-very appreciated)

the point (0,1) does not lie on the curve f(x,y) =e

the point (1,0) lies on that curve make sure you asked the question correctly

no formatting went wrong. but solution is less crucial-i am fine with this part. I am lost with theory. what steps should i use?

I mean algebraicly i can manage whatever, but I just dont und what is asked and what to do

which part? a, b, or c?

a-i just make it all equal to e and plug in point. b and c-no idea

is this a calculus question?

it is as i und next course after calculus

we have not just x and y, but also z. so it is threedomential or how to call it

the plane where x is 0 is the y-z plane.

substitute x =0 and y =1 and find the value of z at that point.

i think it is one step ahead. we are not asked for plane, we asked to find line. so it is (x,y) probably

so you are basically trying to find the slope of the tangent plane at the point (0,1,2)

oh wait hold on.

i have surface. so i need to understand about which curve in this surface we are talking and find tanget line to it in a specific points. that is how i understand it

what you suggest is different-does not look right to me((

the point on the curve is (0,1,2) correct? you need to find the tangent to the curve at that point.

what you suggest is different-does not look right to me((

probably)

btw-tangent line in this case means that i should find partial derivative?

yes

and my next step? lets assume i already got Fx and Fy

my calculus is a bit rusty. let me read up on this. be back in a bit.

sure thank you for your time

did you find out \[f_x and f_y\]?

no yet, should I?

yes

sec

got it

Fx=(e)^(x^2+y)*2x+1/y^2+x*2y

I have never heard about normal vector. which means it probably different material

ignore that.

http://www.math.hmc.edu/calculus/tutorials/tangentplanes/#top

ok

see the example in that.

almost. but again it is different material. it is not tangent plane. we dont work with planes here really. we find curves and work with curves

hmmm

well, I suggest you wait for dumbcow or amistre64 or one of the others. They are good with calculus. Meantime, I'll try and read up on this problem and see if I can help.

my first step-i should understand what is my curve. then i have to find derivative. then plug in values if needed. my main problem-i dont understand how do i know about which curve they are asking and how do i find it. this step from surface to curve is totally unclear for me

then would be nice to understand how do i find one tangent line having two derivatives

your curve is z = (e^x + y) + ln( y^2+ x)

sec

the derivative to that curve will give you a tangent plane.

it is e in a power of x^2+Y plus ln(y^2 +X)

huh?

lol, yes. hard to write it normally

well, whatever the curve is, you get the tangent plane to that curve when you find the derivative of the curve.

it is obvious. but steps are not

oh now I understand the line they are talking about is the line created by the tangent plane to the curve.

no tanget plane here. just lines.

have you done tangent planes before? if not, its kinda hard to visualize.

well, thats the only interpretation I can see of the problem. Maybe Im reading it wrong. sorry couldn't be of more help

I know how does this space looks like. for example circle looks like a huge vase with sticks out of it

but such visualizing does not help me to solve the problem. does not matter. you probably did not cover this yet.

but let me get back to you when I've researched this a bit, but I think my interpretation is right.

ok i will go over notes again.

thank you

oh no, I have done all this about 10 years ago. I don't remember the specifics. Don't use math all that much these days for my job :)

My gosg how old are you? I though everybody here are around 15-20

lol, i'm 25

I am 26

no kidding! are you majoring in math?

It is my first year in university.

oh okay. great! which university?

RRIS, Israel

And as you can guess i finished school 10 years ago-so since that i did not see math at all. now everything from the beggining

oh okay. Yeah, thats a hassle. I don't remember much from what I studied in high school either. well, I hope someone else comes along and helps you out. good luck!

thank you)

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