Find the limit of the rational function a. as x→o and b. as x→-o.x+11f(x) =%3D3x° +12x+11a. lim(Simplify your answer.)%DX→0X + 12x° +x+11(Simplify your answer.)b. lim3X→-oX + 12

Answered: Find the limit of the rational function…

Find the limit of the rational function a. as x→o and b. as x→ – o. x+11 f(x) = x° + 12 x+11 (Simplify your answer.) a. lim Xo X° + 12 x+ 11 b. lim (Simplify your answer.) 3 X- o X + 12

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.6: Rational Functions

Problem 5E

See similar textbooks

Related questions

Q: z2 -6x +36 Find lim I +6 O 36 O 108 The limit does not exist.

A: To find limx→-6x2-6x+36x+6

Q: Given the function f(x) = 5x+ 2x, which is the correct limit to calculate to find f'(x) O A. f'(x) =…

Q: 4.x³+1 d) lim x→-o 2x3+v16x5+1

A: d) limx→-∞4x3+12x3+16x6+1limx→-∞x34+1x32x3+x616+1x6limx→-∞x34+1x32x3+x316+1x6

Q: Using the Nth term test for divergence, V5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to n→∞ 8.

Q: -6x + 3 < f(x) < x² – 6x + 3 Use this to compute the following limit. lim f(x) Answer: What theorem…

Q: given y= f(x)= 2^2-9x+20/x-4 Why is it not possible to apply the quotient limit theroem to find the…

A: Given function is:And the limit of x approaches 4. Hence, the limit is written as: Quotient limit…

Q: Find the limit of the exercise below.

A: Factor the numerator using a^2-b^2=(a+b)(a-b) formula. With a=t and b=4

Q: For n > 0, use Taylor's theorem to find (1+x)!/n – 1 lim 3.

A: Explanation of the answer is as follows

Q: Find the limit of the rational function (a) as x o and (b) as x- -o. Write co or - o Where appropH…

A: Given, fx = 5x3+4x3-x2+x+5 We have to find (a) limx→∞ 5x3 +4x3-x2+x+5 (b) limx→-∞ 5x3…

Q: Find the horizontal asymptotes of the function by computing the limits at infinity.

A: Asymptote of a function is a line the graph of a function approaches. Horizontal asymptote is a line…

Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 2x + 7 x3 – x² + x + 7 f(x)

A: Given that, f(x)=2x3+7x3-x2+x+7 Factoring out x3 on both numerator and denominator we get,…

Q: Find the limit. V17x + h – V17x lim h→0 h

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: _11. If lim (x² +1) = 2, and x = 2.5, then x->-1 lim (x² + 1) is equal to. x-2.5 A. 5.25 C. 6.25 B.…

Q: Find the limit (1+h)3 –1 lim h h→0

Q: f(x) = x² + 3x + 4 f(x + h) – f(x) First, find h |(x^2+2hx+h^2+3x+3h+4)/h Preview Next, simplify the…

Q: find the limit of rational function (a) as x→0 and (b) as x→ -o. 2x + 3 f(x) 5x + 7

A: To evaluate: a)limx→∞2x+35x+7,b)limx→-∞2x+35x+7 Solution: a)limx→∞2x+35x+7 limx→∞2x+35x+7 On…

Q: 2x + 1 If t(x) find lim,-o t(x) %3D 8x + 1

Q: x2 + kx – 10 5. Find the value of k that would make the limit exist. lim f(ax) = x – 2

A: The given limit is limx→2fx=x2+kx-10x-2

Q: The percentage of movie advertising as a share of newspapers' total advertising revenue from 1995 to…

A: Given that: p(t) = −0.07t + 5.0 if t ≤ 3 0.3t + 12.0if t > 3

Q: We consider the rational function f(x) = p(x)/ q(x) = 2x ^2 + cx − 4c / x^2 − x − 2 . Here c is an…

Q: 3. Given the function y = [(x² +2x+ 1]/(x), (x0), find: (a) the limit of y as x approaches positive…

A: Given: The function y=x2+2x+1x, x≠0 To Find: a The limit of y as x approaches positive infinity.b…

Q: 8-3x, for x <1 For parts b) and c), let f(x)= %3D x+x, for x21' b) lim f(x) x→1

A: We have to evaluate limx→1- f(x) For x <1 , f(x) = 8 - 3x

Q: Determine the limit at infinity x+x-6x first.) x+x2-6x lim (x-x2 -6x) (Hint Multiply by O A. 0 OB. 6…

A: To Determine: Compute the limit

Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

A: We will use Chebychev's inequality to find the required limit of probability.

Q: Find the limit. 2 lim 1+ x4 О А. 2 О В. 0о O C. 0 O D. 1

Q: 2. Given the function y = [(x-1)3 – 1]/(x), (x#0), find: (a) the limit of y as x approaches 0. (b)…

Q: 4. Given that f(x)=4x - 3 f (1+h)- ƒ(1) Find lim ,x21

A: Given query is to find the value of indicated operation.

Q: Find the limit of the rational function (a) as x→0o and (b) as x- 0o. Write co or - oo where…

A: The given function is: f(x)=5x+87x+7

Q: -x' B. For f(x)={(x+2)² for -1<x<2,find for x<-1 2x2 for x22 Consider one-Sided Limits to deter a)…

Q: 0, if x is rational f(x) %D 12, if x is irrational and g(x) = 0, S0, if x is rational %3D \x, if x…

A: The given functions are: f(x)=0 ; if x is rational2 ;if x is irrationalandg(x)=0 ; if x is…

Q: Detemine the x- values at which, g(x)= 2x-3x²+x 2x3+5x²-3x is undepined. Evaluate the limit ac x=8…

A: To find: The value of x at which g(x)=2x3-3x2+x2x3+5x2-3x is undefined also evaluate the limit as…

Q: Let ƒ(x) = (3x - 1)/x. Make tables of values of ƒ at values of x that approach c = 0 from above and…

Q: 2O Find the limit of the rational function. lim 25+7-8in 5r 6) Find the Value of flo) such that flx)…

A: 2. a. Given: From the given expression, Thus, the limit of the given funtion is 1/2.

Q: -5x – 2 < f(x) < x² – 5x – 2 Use this to compute the following limit. lim f(x) Answer: What theorem…

A: Limit of the function, by using squeeze theorem

Q: Q1. Find the limit of the function if it exists x² + y² – 2xy lim (x.y)-(0,0) у3 — х3

A: We have to check whether the limx,y→0,0x2+y2−2xyy3−x3 exists or not. Convert the polar coordinates…

Q: Consider the function f(x, y): 5xy 2x2 + y? (a) State the domain of f(x, y). (b) Find the limit 5xy…

A: f(x, y)=5xy2x2+y2A)Domain f(x, y)The function is defined everywhere.Domain: (x, y) ∈ (R×R)

Q: valuate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→−3 x2 + 3x/x2 − 4x…

Q: Find the limit. 2 )X lim 1+ x4 O A. O О В. 1 O C. 0 O D. 2

A: We have to find

Q: Find the limit: -3t e to - 1 t10 – t9' 2+ t -5 lim( t t→0

Q: Find the limit of f(x)

A: Given information

Q: find the limit of f(x)= ((x+h)^3-x^3)/h as h approaches 0

A: SOLUTION-

Q: What result do you obtain when you evaluate the limit (RHL and LHL) of the limit of (x^2-16)/(x-4)…

A: Given f(x)=x2-16x-4 LHL=limx→4-f(x) and RHL=limx→4+f(x) Here if LHL = RHL, then limit exists.

Q: Find the limit of the rational function a. as x→x∞ and b. as x→-. x2 + 11 f(x) = 3 x° + 15 2 + 11 a.…

A: a)

Q: 2. Complete the table by computing f(x) at the given values of x, accurate to five decimal places.…

Q: 22 - 3x + 2 1 3. Find lim as g3 - 2x2 (a) a→0+ (b) T 2+ (c) 2 (d) 2 (e) What if anything can be said…

Q: Forf (x) = 2x +2, compute lim ƒ(1+h) –f (1) %3D f(I+h) -f (1) lim h>0 %D h

A: Given : fx = 2x+2

Q: b. For what value of (k) is the function y=f(x) continuous at x-3. x3-3x2-4x+12 x + 3 x-3 f(x) = %3D…

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Find the limit of the rational function a. as x→o and b. as x→-o.
x+11
f(x) =
%3D
3
x° +12
x+11
a. lim
(Simplify your answer.)
%D
X→0X + 12
x° +
x+11
(Simplify your answer.)
b. lim
3
X→-oX + 12

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Final answer:

Step by step

Solved in 4 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Limits and Continuity$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6 w(x)=x+3x3+6x+9x (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which Of these functions has no vertical asymptote? (d) Which Of these functions has a "hole"? (e) What are the asymptotes of the function r(x) ? (f) Graph y =u(x) , showing clearly any asymptote and x- and y intercepts the function may have. (g) Use long division to find a polynomial P that has the same end behavior as t. graph both P and t on the same screen to verify that they have the sane end behavior.
Match the graph of the rational function f(x)=ax+bcx+d with the given conditions. (a) (b) (c) (d) (i) a0b0c0d0 (ii) a0b0c0d0 (iii) a0b0c0d0 (iv) a0b0c0d0
Now lets use a graphing calculator to get a graph of C=59(F32). By letting F=x and C=y, we obtain Figure 7.15. Pay special attention to the boundaries on x. These values were chosen so that the fraction (Maximumvalueofx)minus(Minimumvalueofx)95 Would be equal to 1. The viewing window of the graphing calculator used to produce Figure 7.15 is 95 pixels dots wide. Therefore, we use 95 as the denominator of the fraction. We chose the boundaries for y to make sure that the cursor would be visible on the screen when we looked for certain values. This was accomplished by setting the aforementioned fraction equal to 1 By moving the cursor to each of the F values, we can complete the table as follows. F 5 5 9 11 12 20 30 45 60 C 21 15 13 12 11 7 1 7 16 The C values are expressed to the nearest degree. Use your calculator and check the values in the table by using the equation C=59(F32).
If the graph of a rational function has a removablediscontinuity, what must be true of the functionalrule?
If the rational function y = r(x) has the horizontal asymptote y = 4, then y →as x→±∞.
find the x- and y-interceptsofthe rational function. (if an answer does not exist, enter DNE.) t(x)=x^2-2x-15/x-9 x-intercept (x,y)= (smaller x-value) x-intercept (x,y)= (larger x-value) y-intercept (x,y)=
If the rational function y = r(x) has the horizontal asymptote y = 9, then y → _____as x → ±∞.
If the rational function y  r1x2 has the horizontalasymptot
If the rational function y=r(x) has the horizontal asymptote y = 8, then y -> ___________ as x -> +infinity
We consider the rational function f(x) = p(x)/ q(x) = 2x ^2 + cx − 4c / x^2 − x − 2 . Here c is an unknown constant. If the limit L = limx→2 f(x) is a finite number, then what is c?
What is the equation for the horizontal asymptote of the rational functional graph? 1) y=2 2)Y=3 3)Y=0 4)X=3 5)X=2 6)X=0
If the rational function y = r(x) has the vertical asymptote x = 3, then as x → 3+, either y → ____(Smaller value) or y →____ (Larger Value)