Question

Find the equation of the tangent plane to the surface z=16y2−0x2 at the point (0,−1,16). Find the equation of the tangent plane to the surface z=16y2−0x2 at the point (0,−1,16). @Mathematics

Answer 1

take gradient of function z

Answer 2

the gradient is vector normal to plane you are trying to find

Answer 3

um....huh?

Answer 4

ok, is that
\[z=16y^2-0x^2\]?

Answer 5

yes

Answer 6

well you can ignore the x part since it is being multiplied by 0
so just z=16y^2

Answer 7

right

Answer 8

rewrite like following
16y^2-z=0

Answer 9

Take gradient
\[{\partial f/dx,\partial f/dy,\partial f/dz}\]

{0,32y,-1}

Answer 10

k

Answer 11

{0,32y,-1} is a vector normal to the plane you are trying to find

plane equation

v(x-a)+w(y-b)+x(z-c)

Answer 12

yea...this is where i get lost

Answer 13

i was with u..and i understand the formula here...but everytime i plug in the values..i get marked incorrect

Answer 14

plug in this point
at the point (0,−1,16)

in here
{0,32y,-1}
plugged in numbers
{0,-32,-1}

Answer 15

v(x)+w(y+1)+t(z-16)
0(x)-32(y+1)-1(z-16)

Answer 16

right so -32y-32-z+16

Answer 17

simplifies to
-32y-z=16

Answer 18

is what i have.....so it's -z = 32y+32-16

Answer 19

and z = -32y +48?

Answer 20

i have to solve it for z =

Answer 21

-32y-z=16
-z=32y+16
z=-32y-16

Answer 22

yea see...says that's incorrect too

Answer 23

lol...helps if i submit it to the correct question

Answer 24

i was tryig to plug the answer into a different question....was correct

Answer 25

you are in calc 3 right?

Answer 26

yea

Answer 27

but i missed an entire week due to being sick so i'm trying to teach myself this

Answer 28

have you started multiple integral yet?

Answer 29

no...we just took a test this past week...we're getting into the chain rule etc. next week

Answer 30

oh, I have to review those because at my school , there is a calc 3 midterm and I am a tutor

Answer 31

wow...ur school has tutor's for calc 3?

Answer 32

no for all math.

Answer 33

my school only goes up to calc 2 for tutors...and like 40 and hour for calc 3 tutors

Answer 34

ours is free up to calc 2...then u gotta pay 40 an hour if you want tutoring for calc 3

Answer 35

I should move to your school then ,

Answer 36

yea really lol..where u go to school at?

Answer 37

U of Illinois
what about you?

Answer 38

unc charlotte

Answer 39

u of illinois is actually on my list to apply for grad schools...u like it up there?

Answer 40

I like big school so it is great

Answer 41

and middle of nowhere

Answer 42

that's what i like

Answer 43

wow, tutors at your school have it made

Answer 44

yea...but we only get paid $9 an hour for other classes....it's until you get to the upper level classes where u actually make money

Answer 45

which nobody wants to spend for so....

Answer 46

I can help up to Linear algebra, and some logic courses

Answer 47

i got 1 more of these i gotta create a new post for :)

Answer 48

if u want some more medals

Answer 49

sure why not