Math

CalculusQ&A LibraryLet f(x,y)= x2-y2a) On the set of xy-axes, draw the level curves L(x,y) = k for k= 1,2,3. On another set of axes, draw the level curves f(x,y)= k for k=1,2,3. (Do this part by hand)b) How do the contour maps in part (a) reflect the fact that L is the linear approximation to f at the point (2,1)? Explain briefly in words.Question

Asked Oct 30, 2019

105 views

Let f(x,y)= x^{2}-y^{2}

a) On the set of xy-axes, draw the level curves L(x,y) = k for k= 1,2,3. On another set of axes, draw the level curves f(x,y)= k for k=1,2,3. (Do this part by hand)

b) How do the contour maps in part (a) reflect the fact that L is the linear approximation to f at the point (2,1)? Explain briefly in words.

Step 1

The level curves ** f (x, y) = k** are just the traces of the graph of

Let ** f (x, y) = x^{2} – y^{2}**, now the level curve

For *k = 1*

Consider the curve *k =**x ^{2} – y^{2 }*

Step 2

Now suppose for k =1

The obtained equation is equation of hyperbola and open up to the left and right, shown in the below diagram:

Step 3

For k = 1, 2, 3, …. The obtained curve is sh...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: step by step on how you would evaluate this function and rounding answer to four decimal places if n...

A: Consider the given function.

Q: Express -x 2dx as aumit X eSS OF ngnt -hard Riemann Sums las the definition Of the indlefmite T cuva...

A: Given integral

Q: Can you please answer number 3

A: Domain is the x values on the graph for which we get a y value. On the picture it shows the x values...

Q: Use an Addition or Subtraction Formula to simplify the equation. sin(3θ) cos(θ) − cos(3θ) sin(θ) = 0...

A: Given expression;

Q: Use the method of partial fraction decomposition to perform the required integration X+2 dx (x-4)2 x...

A: according to partial fraction.

Q: Calculus Question

A: The polar coordinates are,

Q: Problem 1 Parts 1, 2, and 3

A: To determine:Part 1) Approximate value of f(3.01) using linear approximation.Part 2) The actual valu...

Q: Find the derivative.

A: Given function is

Q: Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square incr...

A: Given:Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the squar...