We say that x=-3 is a vertical asymptote of function f, if lim f(x) = 0 А. X + - 3- lim f(x)= - В. x + - 3- lim f(x)= ∞ O C. x- - 3+ С. D. fl-3) is undefined lim f(x)= – ∞ E. X + - 3+

Q: B. Calculate each of the following limits, or explain why it does not converge. i. lim, - 1 (x-2) /…

A: We have given limit, we have to find the value of limit.

Q: The value of the limit 3 lim (1- z/2 is equal to O e-3/2 O e3/2 O e2/3 O 1 The limit does not exist

A: Given: The limit limz→∞1-3zz2.

Q: 5. Consider the limit: lim x² = 16. What is the largest allowable & that will "work" for e = 0.25 in…

A: Given  f(x) = x² To find : Value of delta using definition of limit

Q: Suppose the y =(x) satisfy the following condition lim f(x) - -2 Im x)- , lim f(x) - -3 *--1" lim…

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Q: 6. Find the limit of f(x) = -- 10 as x approaches co and as x approaches - c lim f(x) = X00 (Type a…

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Q: 6. Use the graph of the function f(x) = He to discuss the limit lim 40 f (x). 1+e!/x

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Q: 5) Find the indicated limit if it exists. Vx+4 – 2 a) lim x→0 8x' + 27 b) lim x→-1.5 2x+ 3

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Q: 6. Evaluate the following limits analytically. a. lim 1-4 3x+1 r'- 5x - 6 b. lim 1-6 x - 36 c. lim -…

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Q: Find the Indicated Limit Limh-0(4h5-20h2+2h+1)

A: Given, Limh-0(4h5-20h2+2h+1).

Q: Show that each of the following functions has a horizontal asymptote by calculating the given limit.…

A: As per our guidelines, we are allowed to answer only first three sub-parts of a multiple part…

Q: Consider the following. - 1 if x + 0 f(x) %3D -3 if x = 0 y -2 2 -2 Use the graph to find the limit…

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Q: 3. is a type of discontinuity when the lim and lim f(x) = M where L# M and either f(a) does not…

A: Discontinuity 1: When the limx -> a- f(x) = L and limx -> a- f(x) = M, where L ≠ M and either…

Q: Suppose that f(x) 0 for all a in the interval (-1,1). If lim f(x) = L, then %3D L> 0. For those who…

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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.…

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Q: Consider the following. x² – 2 if x * 0 if x = 0 f(x) = y -2 -1 Use the graph to find the limit…

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Q: 1. Evaluate the following limit: x? -4 a. lim- 1+2x + 2x – 8 (x²-9) 2 b. lim 1+3 (x -3) (t - 3) c.…

A: If putting the value of variable value of function approaches 0/0 we should apply L hospital rule…

Q: 2x+1 if x 2 Determine the one-sided limit lim f(x). x-2- 2

A: The given function is:

Q: When proving the limit lim(x² + 4x - 1) = 11, and e > 0 is given, what is an appropriate choice for…

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Q: 4) Make a table for a sequence of carefully chosen values of a to estimate the limit 1® – 1 f(x) =…

A: By using table value of x for this given function to estimate this given limit

Q: Suppose that g(x) s f(x) < h(x) for all x + 2 and suppose that lim g(x) = lim h(x) = -5. X-2 X-2 Can…

A: It is given that gx≤fx≤hx and limx→2gx=limx→2hx=-5.

Q: 9. There is an infinite discontinuity at x = 0 and f(0) = -2 10. There is a jump discontinuity at x…

A: Explanation of the answer is as follows

Q: Which of the following limits can be evaluated using L'Hôpital's Rule? Зх- 12 A.lim x→4 x2 +16 Зx-12…

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Q: Given that: lim f(x) = 5 x-2 lim f(x) = -5 x--3 lim g(x) = -1 x--2 lim g(x) = -10 x--3 Apply the…

A: To find limx→-38fx+9gx

Q: 2. Given lim= 2, X-2 X Use the precise definition of a limit to find the values of 8 that correspond…

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Q: Given , 3x + 2 f(x) = x - 2 (i) Carikan asimptot mendatar. Find its horizontal asymptotes. Зx+2 Зx+2…

A: We will use rule for calculating asymptotes of a function

Q: Consider the following. x² - 2 if x # -1 if x = -1 f(x) = %3D y -2 -1 1 2 Use the graph to find the…

A: The given function is f(x)=x2-2    if x≠-1-3        if x=-1. Graphically: From the graph, it can be…

Q: A function is said to have a horizontal asymptote if either the limit at infinity exists or the U…

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Q: Given that lim f(x) = 2 .lim g(x) = -4 .lim h(x) = 0 Find the limit lim[h(x) – 39(x) +1]

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Q: Find the maximum value of & > 0 that satisfies the limit claim corresponding to e = 0.3, that is,…

A: In the question it is asked to calculate the maximum value of δ for the given function limx→59-x5=8

Q: Please show step-by-step solutions

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Q: A function is said to have a horizontal asymptote if either the limit at infinity exists or the…

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

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Q: A For the limit lim (x-3x + 4) = 6 illustrate Definition 2 by finding values of d that correspond to…

A: For the limit: limx→2(x3-3x+4)=6, the function is f(x)=x3-3x+4. Now, consider ε=0.2, we have the…

Q: С. 1 Evaluate the following limits x2 +6x+5 1) lim x-5 x²+2x-15 x(х-5)-24 2) lim x→8 x2-8x (2+x)3-8…

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Q: 6. Given f(x)= { 3, if x < -2    x, if -2 ≤ x<8    x+3, if x≥8  estimate lim f(x) x→−2     a.-2…

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Q: 7 x? 4x + 10 if -1 2 if a < -1 | If f (x) = I-1 | - exists. Enter DNE if the limit does not exist.

A: Here we have to find      limx--&gt;-1 f(x) .

Q: 45. a) Find lim h(x). b) Find h(1). c) Is h continuous at x = 1? Why or why not? d) Find lim, h(x).…

A: Given Example -

Q: Find the maximum value of 8 > 0 that satisfies the limit claim corresponding to ɛ = 0.1, that is,…

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Q: 9. Find the limit, if it exists. (If an answer does not exist, enter DNE.) Vx²+x a) lim X--00 -3x

A: topic- limits

Q: 1. Evaluate lim (2x-5) given its graph below. X-2 b. -1 c. 2 d. 1 а. О 2. Given the graph of f(x)…

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Q: - f(x) = -1; lim lim 16. Suppose x-3+ f(x) = -1; and f(-3) is not defined. x-3- Which, if any, of…

A: Given that limx→-3-f(x) =-1 and limx→-3+f(x) =-1. Which implies that limx→-3f(x) =-1. So, Statement…

Q: Find the following limits. √x-3 X-9 x-9 1. lim t²-7t+10 2. lim- t-2 t-2 3. A function f(x) satisfies…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: By definition of limit , find o from the following * lim (-3x – 2) =1 e = 0.03 x→-1

A: Since you have asked multiple questions, we will solve first question for you. If you want other…

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

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Q: A function is said to have a horizontal asymptote if either the limit at infinity exists or the…

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Q: A function is said to have a horizontal asymptote if either the limit at infinity exists or the…

A: Recall: A function is said to be Horizontal Asymptote if either the limit at infinity exists or the…

Q: Q1: Find the limit of the following х-2 2x2+1 tan nx 1) lim- 2) lim x-0 (2-x)(2+x) 3) lim x-2 x²-4

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A function is said to have a horizontal asymptote if either the limit at infinity exists or the…

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Q: With lim f (x) = +o and lim h(x) = -∞ for any a that x→a' x→a is real number, which of the ff. is…

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Q: at x = 1 and f(1) = 4 at x = 2 andf(2) = 3 10. There is a jump discontinuity 9. There is an infinite…

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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.