# am1 - PRINT NAME SOLUTIONS Calculus IV[2443–002 Midterm I...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PRINT NAME: SOLUTIONS Calculus IV [2443–002] Midterm I Q1]... Find an equation for the tangent plane to the graph of f ( x,y ) = x 2 +2 xy- y 2 at the point (2 , 1 , 7) . Ans: Equation is given by ( z- z ) = f x (2 , 1)( x- x ) + f y (2 , 1)( y- y ). We have f x = 2 x + 2 y and f y = 2 x- 2 y which gives us f x (2 , 1) = 6 and f y (2 , 1) = 2. Thus, our equation becomes ( z- 7) = 6( x- 2) + 2( y- 1) which simplifies to z = 6 x + 2 y- 7 . The graph of f ( x,y ) = x 2 + 2 xy- y 2 and the vertical plane y = 1 intersect in a curve. Find a parametric equation for the tangent line to this curve of intersection at the point (2 , 1 , 7) . Ans: We have a point on the line; namely (2 , 1 , 7). We only have to find a parallel vector, V . First, note that V lies in the plane y = 1 and so its y-component will be zero (it is perpendicular to the y-axis). So we can write V = h a, ,b i . Now, the ratio b/a is just the slope of the tangent vector to the curve of intersection in the y = 1 plane. This is just= 1 plane....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

am1 - PRINT NAME SOLUTIONS Calculus IV[2443–002 Midterm I...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online