number 98 in strang and herman calculus 1. Can you provide a full work up as well as an explanation of the steps? I am struggling with finding 0/0 using direct substitution.  https://openstax.org/books/calculus-volume-1@24.1/pages/2-3-the-limit-laws 98.  limh→01a+h−1ah,limh→01a+h−1ah, where a is a non-zero real-valued constant

Q: Find lim (11) O limit does not exist Oe¹-2 Oe¹-4 O2 Other 1/2

A:

Q: Suppose that a function f(x) is defined for all real values of x in [-1,1]. Can anything be said…

A:

Q: Prove lim(3x – 2)=7. (Hint: Use the 8 – e definition of the limit.) |

A: Given:  limx→3 3x-2 =7Definition: ε-δ definition of a limits:∀ ε>0 , ∃  δ…

Q: See pencil for correction of problem

A: First we simplify the expression (x2-2x-8)/(x+2)=(x2-4x+2x-8)/(x+2)…

Q: Formally prove that lim 2x+3=7 using the ɛ,8 definition of a limit. x→2

A:

Q: Consider the function g(x) = cos(1/x). We will investigate the limit behavior at x = 0. c) If n is…

A: Given function,

Q: Show that the limit does not exist: limit    (x^2+y-2)/(x-2y+4)                    (?,?)→(0,2) I…

A:

Q: Evaluate lim z²-4z+3 z-3 O 1 O 3 O limit does not exist

A: Given function is, limx→3x3-4x+3x-3

Q: 4. Evaluate lim [In(2+x)-In(1+2.x)] using Calculus 1 limit techniques. Show all steps to justify…

A: To evaluate: limx→∞ln2+x-ln1+2x Solution: We know that, lna-lnb=lnab Therefore,…

Q: 3. Evaluate this limit. x + 4 lim x--4 4x + 16

A: given,

Q: Calculate each of the following limits, or explain why it does not converge. You may use any…

A:

Q: Use l'Hopital's Rule to evaluate the limit. cos 3x - 1 x2 21) lim x-0 A) - C) 0 D en len

A:

Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim 2 x→1 x´ + x -2

A:

Q: 1) DRAW THE GRAPH OF A FUNCTION WHERE lim,-af(x) DOES NOT EXIST FOR SOME INTEGER a. EXPLAIN WHY THE…

A:

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: given find the limit numerically limx→23x−95x−25

Q: The limit as x approaches infinty of (x+3^x)/(x^2-3^x) Evaulate using L'Hospital's Rule providing a…

A:

Q: (3) It is a true fact that lim 142 5x – 7 The e-d proof for this limit given below contains a…

A: We have to find the incorrect step in the ε‐δ proof of the given limit which is limx→2 35x-7=1.…

Q: How does the sandwich theorem enable us to calculate a variety of limits?

A: Sandwich theorem: Consider 3 function f(x),gx,hx such that fx≤gx≤hx. Also, assume that limx→cf(x)=L…

Q: 8. The function f(x) = 4 – x² is both continuous and differ- entiable at x = 1. Write these facts as…

A: Given that the function f(x)=4-x2 is both continuous and differentiable at x=1. To write these facts…

Q: 3. Determine the infinite limit. x² + 3x lim x--1- x2 + 2x + 1

A:

Q: 1) Describe in your own words, how to determine the limit of f(x) as x approaches a given point and…

A: Hi! you have posted multiple questions. As per norms, we are answering the first question as nothing…

Q: Determine the limit: lim 1+n-'sin3(n) А. С. -1 1, B.

A: Introduction: When we deal with sine or cosine function in limits, we follow the inequality sinx≤1.…

Q: limit as x---3 for the function (x-2)^11/(3-x) using L'Hopitals.

A: Consider the given function (x-2)11 / (3-x).

Q: limit as h---0 for the funtion ((e^2h)-1)/h using L'Hopitals

A: We need to evaluate the given limit using L'hopitals rule. As per L'hopitals rule, if we get 0/0 or…

Q: 13. State what it means for a function f to be continuous at a point x = c, in terms of the…

A: We have to state the meaning for a function f to be continuous at a point x=c ,in terms of the ε-δ…

Q: Broadly speaking, what are the Limit Laws, and why do they help us calculate limits? 2. In Example…

A: 1.) Limit laws are very helpful in calculus i will explain you how.Suppose you know the limit of one…

Q: 1+n Prove using the definition of the limit that limn→∞ 1-2n 2

A:

Q: . Find two sequences {an}o and {b»}_o such that lim 0o. As part of your solution, explain…

A:

Q: compute limit as x goes to infinity of xe^-x

A: Given,            limx→∞x e-x

Q: If lim f(x) and lim f(x) exist but are not equal, then x = c is a(n) jump discontinuity. X-C- XC+ If…

A:

Q: Prove lim 7-x =6 using the ɛ,8 definition (precise definition) of a limit. x2 2

A: Given data:     The given expression for the limit of the function is: .   The given expression for…

Q: How do you approximate a limit numerically AND graphically?

A: We always evaluate limits from both the left and right directions and if they match, then, the limit…

Q: 10. Prove that lim x2 = 4 using the epsilon-delta definition of a limit. %3D X-2

A: limx→2x2=4

Q: 4 Using the e- 8 definition of limit, prove that lim I-3 3r 1 2 -

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 7. Compute the limit to infinity: 4-2+3r+1 a lim 7+3r-r+ 12

A:

Q: 1-√3-x 4. lim. x→2 4-x²

A:

Q: 5.3. Show that when a limit of a function f(z) exists at a point 2o, it is unique.

A:

Q: 5) Prove that the order of iteration of limits can be significant by showing that х2 lim(lim у-0…

A: It is needed to prove that order of iteration of limits can be significant by showing that:

Q: 16. lim (2 – 3x) = –4 x 2 %3D

A:

Q: In(3x) EXAMPLE 3 Calculate lim SOLUTION Since In(3x) → o and → o as x - o, l'Hospital's Rule…

A: Given:         limx→∞ln3xx3 L'Hospital's Rule:         limx→cfxgx=limx→cf'(x)g'(x)  Since ln(3x)→∞…

Q: Which of the following limit laws is NOT applied? lim (2? + 7æ – 5) = 13 O Limit of a Constant O…

A: laws of limit

Q: (a). Show that limit x→1, does not exist if (3-2х for x<1 f(x) = { 6x-4 for x21

A:

Q: 6 -- if a - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

A:

Q: (a) Find the limit (if exist): lim "(2t-2)2 dt 2x-1

A:

Q: State the value of each of the quantites below. A) limx---> -4^-   F(x)= B) limx---> -4   F(x)=…

A:

Q: lim sec(4+x?)' Ax where Ax = 12-(-3) and x; = -3+iAx.

A:

Q: 2. Compute each limit below using limit laws. 7+3x (a) lim 7+3x (b) lim r-4 4-x 7+3x 4-X

A: we have to find the following limit

Q: Compute the following limit.“ KC'arctan(2t³ – 1) dt] du (x – 1) In r lim Be sure to explicitly…

A: We have to evaluate a limit and we will use the L'hospital's Rule to find the answer.

Q: 5) Find the indicated limit if it exist. а) lim X-2 3- Vx+ 7 2 - x x' +1 b) lim x-- x+1

A:

Q: Prove the statement using the ɛ, 8 definition of a limit. lim (x2 – 2) = 7 x- -3 Given ɛ > 0, we…

A:

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.