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Chapter 10: Q. 48 (page 790)

Graph the quadric surfaces given by the equations
$z = x^{2} + y^{2}$

Short Answer

Expert verified

The surface graph is a cone, as shown below.

Step by step solution

Introduction.

Quadric surfaces are described in two dimensions by quadratic equations. Quadrics include spheres, ellipsoids and cones.

Given Information.

Consider the following formula:

$z = x^{2} + y^{2}$

The goal is to create a graph of the quadric surface.

Explanation.

The surface graph is a cone, as shown below.

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Most popular questions from this chapter

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

$u \times w and w \times u$

Suppose f and g are functions such that $\lim_{x \to 3} f (x) = 5, \lim_{x \to 4} f (x) = 2$ and $\lim_{x \to 3} g (x) = 4$

Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.

$\lim_{x \to 3} - 2 f (x)$

Find a vector in the direction of $<- 1, 2, 3>$ with magnitude 3.

Calculate the limits in Exercises $25 - 28$ , using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.

localid="1648227587052" $\lim_{x \to 0} \frac{3}{2 x^{2} - 4 x + 1}$ .

In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

$P (3, 1, 8), Q (0, 6, - 1), R (- 3, 5, - 3)$

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Graph the quadric surfaces given by the equations
$z = x^{2} + y^{2}$

Short Answer

Step by step solution

Introduction.

Given Information.

Explanation.

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Graph the quadric surfaces given by the equationsz=x2+y2

Short Answer

Step by step solution

Introduction.

Given Information.

Explanation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Pure Maths

Discrete Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Graph the quadric surfaces given by the equations
$z = x^{2} + y^{2}$