Question: We explore functions whose graphs approach a nonhorizontal line as x . A line y = ax + b is called a slant asymptote

We explore functions whose graphs approach a nonhorizontal line as x → ∞. A line y = ax + b is called a slant asymptote if

or lim (f(x) (ax+b)) = 0 X-00 lim (f(x) (ax + b)) = 0 X--0

If ƒ(x) = P(x)/Q(x), where P and Q are polynomials of degrees m + 1 and m, then by long division, we can write

f(x) = (ax + b) + P(x)/Q(x)

where P1 is a polynomial of degree

(a) y = Tou zx x + 2 (b) y = x + x x + x + 1

or lim (f(x) (ax+b)) = 0 X-00 lim (f(x) (ax + b)) = 0 X--0

Step by Step Solution

★★★★★

3.58 Rating (151 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since degP deg Q Thus and y ax b is a slant asymp... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Q:

We explore functions whose graphs approach a nonhorizontal line as x . A line y = ax + b is called a slant asymptote if Sketch the graph of Proceed as in the previous exercise to find the slant...

Q:

We explore functions whose graphs approach a nonhorizontal line as x . A line y = ax + b is called a slant asymptote if Show that y = 3x is a slant asymptote for (x) = 3x + x 2 . Determine whether...

Q:

We explore functions whose graphs approach a nonhorizontal line as x . A line y = ax + b is called a slant asymptote if Sketch the graph of or lim (f(x) (ax+b)) = 0 X-00 lim (f(x) (ax + b)) = 0 X--0

Q:

2.5 EXERCISES 1-6 . Write the composite function in the form f(g(x)). 15. y = x sec kx 16. y = 3 cot ne [Identify the inner function u = g(x) and the outer function y = f(u).] Then find the...

Q:

ECET2e Section 2.4 21/10/2016, 02:30 WebAssign ECET2e Section 2.4 (Homework) Current Score : 6 / 16 Thu Aung MATH-UA 121, section 11, Fall 2016 Instructor: Benjamin Harrop-Griffiths Due : Thursday,...

Q:

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

Q:

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

Q:

Reference: Calculus and Its Applications, 12th, by Marvin L. Bittinger and David Ellenbogen Book Elementary Applied Calculus I need help with questions These are practice questions Links to Book...

Q:

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

Q:

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

Q:

The manager of K&K Ltd is considering a new investment opportunity at the end of December 2020. The company has two independent divisions: Division A and Division B. Any of these divisions can take...

Q:

Based on the following transactions, calculate the revenues and expenses that would be reported (a) On the cash basis (b) On the accrual basis: i. Credit sales to customers totalled $35,000. ii. Cash...

Q:

Question 1 1 5 pts Choose all of the following statements that are correct. The slope of the security market line is determined by risk aversion. The intercept of the security market line is the rate...

Q:

Using the information in Problem 7, what would be the effect of adding another person to the workforce? Specifically, this means increasing the number of workers from 38 to 39. Compare various costs...

Q:

As in Section 6.6, Exercises 45 and 46, the p.d.f. for the waiting time X until an event occurs often follows the exponential distribution, with the form g(x) = e-x for some positive value of ,...

Q:

A 20 kg child is the end of a long see saw, 3 m to the right of center. An 80 kg adult is 1 m to the left of center. Find the center of mass. Who will go up? The formula for the expectation in...

Q:

A 20 kg child is 3 m to the right of center, her 30 kg older brother is 1 m to the right of center, and an 80 kg adult is 1 m to the left of center. Find the center of mass. Who will go up? The...

Q:

Consider a language similar to markup languages. Text is annotated by tags that are in the form text/ The label and following words are composed of letters. There is always a label with zero to many...

Q:

, Inc. has cash of $36,000, supplies costing $1,500, and stockholders' equity of $28,000. Determine the liabilities of the business. Write the accounting equation for Boehms, Inc. Start by writing...

Q:

You own $15,370 of Opsware, Incorporated stock that has a beta of 4.08. You also own $23,320 of Lowes Companies (beta = 1.57) and $14,310 of New York Times (beta = 1.02). Assume that the market...