what can be stated about the graph of f(x) given  lim     f(x)=2/3 x→−∞   a. f(x) has a horizontal aymptote aat y=2/3 b.f(x) has no horizontal asymptotes c.f(x) has no vertical asymptotes d.f(x) is discontinuos when x=2/3

Q: Find the limits in Exercises

A: To find,   limθ→∞cosθ-1θ  Let y=limθ→∞cosθ-1θ Limit is tending towards positive infinity, let us try…

Q: 3) If lim d(t) = 5, can there be a vertical asymptote in the graph of d(t) at t= 0?

A:

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the vertical asymptotes?

A: Given function is,

Q: Theory and Examples

A:

Q: x2 - 9 The following problems concern the behavior of the rational function f(x) = (x +2)(x +3)(x-…

A: By Bartleby guidelines I can only answer the first three sub-questions of the given problem.

Q: 1) Find the Limit lim/→0 3x²h-7th+h h

A:

Q: Match the values on the top with the given limit. A -o BO C 8/9 D +co 9 x2+12 x +9 lim 64 - x2 X- 8-…

A:

Q: The graph of the function f(x) = tan a is given above for the interval z e [0, 27] ONLY. Determine…

A: Given

Q: Find a & that works for & = 0.1 for the following limit. lim 6x + 7 = 13 x1

A: The limit is given by limx→16x+7 = 13 To evaluate: The value of a δ that works for ε=0.1

Q: Consider the following. lim (4 – x) X→3 y 3 2 1 2 4 Use the graph to find the limit (if it exists).…

A:

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

A:

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: lim 4e-4x lim 5ex - 4 X-4 9x + 7x - 7 lim 2x2 - 2x X- +0

A:

Q: ) Find the value of k that makes function continuous at ¤ =4 f(x) = { | 2x +7 > 4 6x -k < 4 (i) If…

A:

Q: find the limit of g(x) as x approaches the indicated value.

A: the given expression is: limx→51x+g(x)=2

Q: Recall that J x+ 4 |x +4| = ((x+4) X <-4. Therefore, we will need to check the limits when…

A: NOTE: Refresh your page if you can't see any equations. . as we know,

Q: Please

A:

Q: find the limit of g(x) as x approaches the indicated value.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

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

A:

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

A: given function is                                      given graph is…

Q: 1. Find the following limits. e3r lim 3.x е (a) (b) lim e3/(2-a) lim In(1x2 - In(1 x (c) _ (d) lim…

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Q: b. If f(1) is undefined then f (x ) has a vertical asymptote at x = 1. lim f(x) c. If exists, then…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

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

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

A:

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: 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: for |x| > 1, 2x2 fx,(x) = 0, %3D otherwise. Let L = lim P(max{X1,..., X,} < n log(v5)). Determine…

A: Let Xn be a sequence of random variables such that,

Q: 6. Given the graph of g(x) below, evaluate lim (g(x)) x→4 -3- -2- 4 -1- DNE (does not exist) 4 -1…

A: Thats easy. Have a good day!!!

Q: 4. The graph of a function f(x) is shown at right. If g(x) = V1+ 3x , find lim [f(x) + 3 g(x)]. %3D…

A: The graph of the function fx is given. From that graph it is clear that, the function fx, at x=1…

Q: For the function f(x) = arctan 1 which is graphed on desmos. (a) Compute lim f(x) (b) Compute lim…

A:

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: Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999,…

A: First, we factor numerator and denominator. Then we simplify for x not equal to 3. Then use this…

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: Find the limit analytically: 2-4x lim 40 5+3x x? - 2.x -15 lim x 5 2. 3. Find dy/dx of:

A: A number M is said to be the limit of a function f(x) at x=a if for any arbitrarily chosen positive…

Q: 1. Investigate the limiting behaviour of x2 lim (x,y)¬(0,0) x2 +3xy +y2

A: It given function fx,y=x2x2+3xy+y2. When x,y=0,0 in fx,y=x2x2+3xy+y2 will result in 00. Set the…

Q: M 27. (a) By graphing the function f(x) (cos 2x- cos x)/x %3D and zooming in toward the point where…

A: Given function f(x)=cos2x−cosxx2

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,…

A:

Q: Find the limit of f(x)

A: Given information

Q: 2. Use the given values to set up a table to evaluate the limits. Round your solutions to sin 3x…

A: limx→0sin3xx

Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: Find the limit. lim (e 4/x+ 9x) x/2 x-0 0 1 00 e2

A:

Q: 13. Given the function f (x) = 2xv1 – x2. Determine the - c. Y intercept d. Vertical Asymptote(s)…

A:

Q: e. The functions In x100 and In x have comparable growth rates as x→0o. Is the statement true or…

A:

Q: 3. As x approaches o, the graph has a: +x lim 4x -x* ORemovable discontinuity (hole) OJump…

A: Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to…

Q: Find the limit of f(x) = 6 - 2 as x approaches o and as x approaches - o. lim f(x) = %3D (Type a…

A:

Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

A:

Q: 3x – 1, if x 8 | Let f(x) = { 5 x+9 Show that f(x) has a jump discontinuity at x = 8 by calculating…

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.