Determine whether y → ∞ or y → -∞ as x → -∞ and x → ∞. Determine whether y → * or y → - as x- * and x→ *,y= -x2 + 7x3 - 6x - 4O y-* as x- . y-. as x- *O y- as x- ; y- as x-O y- as x--y- as x-y- as x- .* y- as x- a

Determine whether y → ** or y → -* as x- * and x- *. y= -7x2 + 7x3 + 6x - 4 O y- * as x- .*; y - . as x- * O y- * as x→ -#; y- = as x → a O y-. as x- *; y * as x → * O y- as x- y- as x-

Determine whether y → ** or y → -* as x- * and x- . y= -7x2 + 7x3 + 6x - 4 O y- as x- .; y - . as x- O y- * as x→ -#; y- = as x → a O y-. as x- ; y as x → * O y- as x- y- as x-

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 26E: Determine whether the set S={2x+x2,8+x3,x2+x3,4+x2} spans P3.

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Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Question

Determine whether y → ∞ or y → -∞ as x → -∞ and x → ∞.

Expert Solution

Step 1

Given function :

$y = - 7 x^{2} + 7 x^{3} + 6 x - 4$

To determine the limit of y we need to substitute the limit of x and then solve.

Step 2

When $x = - \infty$

$- 7 {(- \infty)}^{2} + 7 {(- \infty)}^{3} + 6 (- \infty) - 4 = \infty - \infty - \infty y \to - \infty$

When $x = \infty$

Then,

$y = - 7 {(\infty)}^{2} + 7 {(\infty)}^{3} + 6 (\infty) - 4 = \infty + \infty + \infty y \to \infty$

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