5

Froblenj 2 ([email protected] poits) Find an equation of tbe tangent plane to tbe surface at the given point 2 +22 zy + 622 =10, P(2,1,1)...

Question

Froblenj 2 ([email protected] poits) Find an equation of tbe tangent plane to tbe surface at the given point 2 +22 zy + 622 =10, P(2,1,1)

Froblenj 2 ([email protected] poits) Find an equation of tbe tangent plane to tbe surface at the given point 2 +22 zy + 622 =10, P(2,1,1)



Answers

$1-6$ Find an equation of the tangent plane to the given surface at
the specified point.
$$z=(x+2)^{2}-2(y-1)^{2}-5, \quad(2,3,3)$$

Were given a surface and a point on the surface and were asked to find an equation of the tangent plane to the surface. At this point, the surface has equations equals three times X minus one squared, plus two times why plus three squared plus seven. And the point is to negative 2 12 right away. We see the weekend rates C as a function of X and y se F, which is three times X minus one squared, plus two times why plus three squared plus seven. And therefore it follows that the partial derivative F with respect to X this is six times X minus one in the partial derivative f with respect to why is four times why plus three. Therefore the partial derivative of F with respect to X, evaluated at a point which has X Y coordinates to negative two. This is six the partial derivative of F with respect to y at too negative, too. This is four, therefore, by Equation two. Equation for the Tangent plane is Z minus. The Z value over point 12 equals partial derivative of F with respect to x Too negative, too. Times X minus the X value of her point, which is to plus the partial derivative of F with respect to y at too negative, too. Times y minus the Y value over point, which is negative. Two and substitution and simplifications give us Z minus 12 equals six times X minus two plus four times Why plus two and rearranging. We get that Z is equal to six x plus four y, and then the constant term is eight.

This question asks us to solve for the tangent plane given a point and the plane to do this, we first need to know how to find a tangent plane. The equation for a tangent plane is T. Is equal to F sub X. At a comma B times x minus a plus F sub Y. At a Cumbie times y minus B plus z at a comma B. So from here we can solve. So our F sub X is for X under F sub Y Is two, Y -5. Well or point is 1:02 -4. So if we plug in or point, we get the F sub X at a comma B is four. Never F sub Y at a comma B is negative one. So now we have that. Plus we have our playing so we can plug it into the equation. We have T is equal 24 times x minus a. And a is one plus negative one Times Why -7. & B is too plus Hersey at a comma B. Well rz at a column B is just value given to us at the point and the value given to us at the point is negative for so from here we can simplify so we'll bring this up here and so to simplify, we can bring out Or we can multiply out our four. So we have four X -4 -Y plus two minus four. And if we simplify even further, we get the T. Is equal to four X minus y minus six.

Were given a surface and appoint and rest to find an equation of the tangent plane to the surface. At this point, surface has the equation three y squared minus two x squared plus X. The point on the surface is too negative. One negative three. Yeah, well, right away. Noticed. Weaken right the as a function of X in y as Z equals three y squared minus two x squared plus X And therefore we have that the partial derivative f with respect to X is negative four x plus one and the partial derivative f with respect to why is six y so it follows that at our point to negative one negative three partial derivative with respect to X. Well, this is had to negative one which is negative. Seven. The partial derivative of F respect toe Why at two negative one is negative six. Therefore by equation two from this section. Vision for the tangent plane is Z minus and then rz value, which is negative three for this point, equals partial derivative of F with respect to x Evaluated A to negative one times X minus Our X value, which is to plus the partial derivative f with respect to why evaluated at two negative one times why minus or why value, which is negative one? Or why plus one and simplifying. We get Z plus three equals on the right hand side. We have negative seven times X minus two, minus six times Why plus one rearranging yet Z equals negative seven x minus six y and the constant term is simply five.

For this problem, we are asked to find an equation of the tangent plane to the surface, X squared plus Y squared equals one at the 10.100. So the first thing that we want to do is find the gradient of our function and evaluate it at the given point. So we want gradient of F 100. So first I'll write our gradient as a column vector with just in terms of X and Y. So would be to X two Y zero. We're evaluating it at the .100. So That will just give us 200 as our gradient, which means that we can define our tangent plane as F of X. Y. Zed is equal to two times X -1 Equals zero. That defines our plane.


Similar Solved Questions

5 answers
1 . Which of the following structures represent the same carbohydrate (i.e are identical)? CHO CHO OH HO- OH HO_ HO= HO" HO CHzOH CHzOHonly and 2 b. only and 3 only 2 and 3 d 2 and 3 None of them are identical:
1 . Which of the following structures represent the same carbohydrate (i.e are identical)? CHO CHO OH HO- OH HO_ HO= HO" HO CHzOH CHzOH only and 2 b. only and 3 only 2 and 3 d 2 and 3 None of them are identical:...
5 answers
1) a is on the diagonal, b otherwisc,det
1) a is on the diagonal, b otherwisc, det...
5 answers
Frjber " J87t RonUer" PruzalalCuarkd U>J+4SEh09 Y 0+€ 2er # JOln+* {i 19 3MAeT2bi Er44NufnA >Ehlier uIiie 5+#26
Frjber " J87t Ron Uer" Pruzalal Cuarkd U> J+4 SEh 09 Y 0+€ 2er # JOln+* {i 19 3 MAeT 2bi Er44NufnA > Ehlier u Iiie 5+#26...
5 answers
Tne graph of the function y-fx} is shown: Fill in each blank with yefix)cepencing on whether the quantity is positive, negative Or zero_2 fS)3. f S)4. f"(5}ft8. f"(T)
Tne graph of the function y-fx} is shown: Fill in each blank with yefix) cepencing on whether the quantity is positive, negative Or zero_ 2 fS) 3. f S) 4. f"(5} ft 8. f"(T)...
5 answers
(2s +12) c) Fi(s) = (s- + 25+5)(s" + 25+3) d) Fa (s) =- (s+1)"
(2s +12) c) Fi(s) = (s- + 25+5) (s" + 25+3) d) Fa (s) =- (s+1)"...
5 answers
D Question 62 ptsA researcher believes that the proportion of women who exercise with a friend is greater than the proportion of men. He takes random sample from each population and records the response to the question_ 'Have vou exercised with a friend at least once in the last seven days?" The null hypothesis is Ho: Pwomen-Pmen: Choose the correct alternative hypothesisHa; Pwoment PmenHa: pHa; Pwomen PmenHa; Pwomen Pmen
D Question 6 2 pts A researcher believes that the proportion of women who exercise with a friend is greater than the proportion of men. He takes random sample from each population and records the response to the question_ 'Have vou exercised with a friend at least once in the last seven days?&q...
5 answers
EnCuea frelqAoMuh parac/+ermin? 0-8241-457 3 J : aJelez;
EnCuea frelqAoMuh parac/+ermin? 0-8241-457 3 J : aJelez;...
5 answers
Find a sine function whose graph matches the given curve.
Find a sine function whose graph matches the given curve....
1 answers
Does the silicate hedenbergite, CaFeSi_ $\mathrm{O}_{6},$ contain single-stranded or double-stranded silicate chains? (Draw comparisons with Figures 19.6 and 19.7 )
Does the silicate hedenbergite, CaFeSi_ $\mathrm{O}_{6},$ contain single-stranded or double-stranded silicate chains? (Draw comparisons with Figures 19.6 and 19.7 )...
5 answers
A gas mixture has partial pressures of 148 mmHg O2, 270 mmHg Ne,and 518 mmHg SF6. What is the mole fraction of oxygen in themixture?
A gas mixture has partial pressures of 148 mmHg O2, 270 mmHg Ne, and 518 mmHg SF6. What is the mole fraction of oxygen in the mixture?...
5 answers
Some sort of $ definitely = follows consumed in my life using the logistic = growth The number of cinnamon rolls have cinnamon roll consumption have eaten and of cinnamon rolls shaped curve: If | can Odel my lifetime 3000 where flx) is the total number E function f (x) I+1000e 0.25x 1988. Answer the following point in my life? (2019) x is the number of years after consumed at this How many cinnamon rolls have
some sort of $ definitely = follows consumed in my life using the logistic = growth The number of cinnamon rolls have cinnamon roll consumption have eaten and of cinnamon rolls shaped curve: If | can Odel my lifetime 3000 where flx) is the total number E function f (x) I+1000e 0.25x 1988. Answer th...
5 answers
Show that if the sum: S - a1 -a2 -...an is an entire number even and allthe terms a1,...,an are odd whole numbers, so n is even.You can use the following proposals without proving them. If youwant to use other proposals, you have to prove them.- The sum of pair numbers is even.- The sum of two odd numbers is even.- The sum of an even number and an odd number is odd.
Show that if the sum: S - a1 -a2 -...an is an entire number even and all the terms a1,...,an are odd whole numbers, so n is even. You can use the following proposals without proving them. If you want to use other proposals, you have to prove them. - The sum of pair number...
5 answers
What the frequency of light hertzrelength of 3.76 x 10-7m?
What the frequency of light hertz relength of 3.76 x 10-7m?...

-- 0.019671--