## Related questions with answers

Question

Find equations for the tangent plane and normal line to the surface given at the prescribed point.

$x^{3}+2 x y^{2}-7 x^{3}+3 y+1={0} \text { at } P_{0}(1,1,1)$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 4We have to find the equation of the tangent plane and normal line to the curve

$x^3+2xy^2-7x^3+3y+1=0,$

at $P_0(1,1,1)$. Let $F(x,y)=x^3+2xy^2-7x^3+3y+1$, and consider $C$ to be the level curve $F(x,y)=0$. The gradient $\nabla F$ is normal to $C$ at $P_0$. First we find the gradient of $F$ which is

$\nabla F(x,y)=F_x(x,y)\textbf{i}+F_y(x,y)\textbf{j}.$

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

#### Thomas' Calculus

14th Edition•ISBN: 9780134438986Christopher E Heil, Joel R. Hass, Maurice D. Weir10,144 solutions

#### Calculus: Early Transcendentals

8th Edition•ISBN: 9781285741550 (3 more)James Stewart11,084 solutions

#### Calculus: Early Transcendentals

9th Edition•ISBN: 9781337613927 (3 more)Daniel K. Clegg, James Stewart, Saleem Watson11,049 solutions

#### Calculus

6th Edition•ISBN: 9781465208880 (1 more)Karl J. Smith, Magdalena D. Toda, Monty J. Strauss5,412 solutions

## More related questions

- physics
- physical science

1/4

- physics
- physical science

1/7