Show that each of the following functions has a horizontal asymptote by calculating the given limit. -3x lim r-00 15 + 2x 10x – 13 lim x→-00 x3 + 2x – 13 x2 – 2x – 12 lim - 14 13x?

Q: Find o for e = 0.1 for the following limit. %3D lim 3x - 4 = 17

A: ε=0.1 and limx→7 3x-4=17

Q: Q3: Find the limit for the following functions: - 4 1- lim(- x→2 x-2 - x2 -4 2- lim(x – Vx2 + x) x-1

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Q: Use the graph of the greatest integer function, y = [x], to find the limits given below. Ay 4- [0]…

A: [.] the greatest integer function returns the closest integer less than or equal to the given…

Q: 1 (i) lim 3n2 – 4000 のlim(- 2n2 +10000 X00

A: Topic:- calculus

Q: Find the limit. (If an answer does not exist, enter DNE.) (x + Ax)² – 5(x + Ax) + 3 − (x² − 5x + 3)…

A: Given :lim∆x→0x+∆x2-5x+∆x+3-x2-5x+3∆x

Q: Find the limits from the given graph of f(). -2-1 1 2 3 4 S lim f(x) T0-

A: The graph of the function fx is given as ,

Q: Evaluate the limit of the given functions. 3x² - 17x+ 20 25x + 36 1. 2. lim x+44x² t³-1 1 lim t-1…

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Q: Find the limit of the following function ex (a) lim x0 e1/x+1 (b) lim f(x), where f(x) = { 3x – 2,…

A: To find the limits

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: Consider the following. Sx² - 1 f(x) if x + 0 -3 if x = 0 y 1 -2 2 -2 Use the graph to find the…

A:

Q: se the graph of the given function f to determine the limit at the indicated value of a, if it…

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

Q: Use the graph of the given function f to determine the limit at the Indicated Value df y3f(x) 3+ -3…

A: From the given graph;

Q: For what value of the constant k such that the following limit exist: 2x+x lim |(x² – 2+k)

A: We have to find the limit of the function 2x+xxx2-2+k as x tends to 0, where |x| denotes the…

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: Find lim f(x) for the given piecewise function. x-4 2x +2 if x 4 If the limit does not exist, enter…

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Q: Use the graph of the given function f to determine the limit at the indicated value of a, if it…

A: Graph of the function is given, we have to find the limit at x=a

Q: 1 (1+ h)² + 1 lim x-0 x2 – 1 lim h-3

A: limx→ 0x3-1x2-1Plug in the value x=0=03-102-1=1

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

A:

Q: Consider the following. 1(x) = {x²-1 -2 If x 1 If x= 1 y X Use the graph to find the limit below (if…

A: The given function is f(x)=x2-1  if x≠1-2      if x=1We have to find the function value at x=1

Q: lim xラ lim (-5th)=2 hフ0 X -5 り

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Q: Q4\ find limit of the following 1- lim x² -2 Jx-2

A: We have to find the value of limx→2x2-2x-2 Substitute x=2     =22-22-2=4-20=20=∞

Q: Find the limit of the following: lim     e(2/3-x) x→3+

A: To evaluate the below right-hand limit

Q: Find the limit for the following fune V1+x-1 lim 1)

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

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: Find the following limit: lim f(x) X-2 ОА. 2 О В. -2 OC. 0 O D. The limit does not exist

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Q: I need help solving this.

A: The given function is a piecewise function and it is required to calculate following limit,

Q: Consider the following. Use the graph to find the limit below (if it exists). (If an answer does not…

A: The limit exists 0.

Q: Determine the limit value of each of the following functions 11. lim 5(3x + 2) x →-1 12. lim * x→ 4…

A: Tp evaluate the given limits.

Q: 2. lim (e* – 1)lnx X0+

A:

Q: For the function 0 < x < 4 = 4 2x – 4, -2, f(x) = x2 – 8x + 20, 4< x use algebra to find each of the…

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Q: se the graph of the given function f to determine the limit at the indicated value of a, if it…

A:

Q: Find lim f(x) for the given piecewise function. 2x + 1 if x 6 If the limit does not exist, enter…

A: Solution is given below:

Q: Please see attached -

A:

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: Solve the following limit by definition (ii) lim f (x) = 2 if f(x) : (4 – 2x, x 1 x-1

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Q: Find the following limit: lim f(x) X-3 O A. 0 В. 1 O C. -3 O D. The limit does not exist

A: Let's find the following limit.

Q: Give the formula for a function f(x) that has a vertical asymptote at x = -6 so the left hand limit…

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

A:

Q: Q1:- Find the limit for each of the following functions if is exist ? 1) lim|x – 3| x-3 sx + 2 ,…

A: We find limit of given function

Q: Find the following limit: lim f(x) X-1+ O A. -1 Ов. 1 ОС. 3 O D. The limit does not exist

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Q: Draw the graph of f(x) = E, and annotate the graph to indicate the meaning of I-2 lim - 2| T→2 x – 2…

A: We have to find limit

Q: Evaluate the left hand and right hand limits of the function defined by (1+x, if 0 1 at x 1. Also…

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Q: Q3: Find the limit for the following functions: - Vx-2 1- lim x-4 x-4 (2x-3)(Vx-1) 2- lim x→1…

A: Apply d'hopital rule

Q: 3 4. lim = 1 1 х-3 ух — 2 — V4 — х 12. х2 — 1, 2 1 5. lim х-з \x — 1

A: Given that: 4. limx→3x-3x-2-4-x=15. limx→31x-1-2x2-1=12

Q: 4. Evaluate the following limit functions 2x-3x+1 а. lim x-3 5x+4 x²-3x b. lim x-3 2x2-5x-3 C. lim…

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Q: Find lim f(x) for the given piecewise function. 2x +3 f(x) = { 5 -*+18 if x > 6 if x < 6 %3D if x =…

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Q: Determine the following limits at infinity. f1x2 xSo g1x2 lim if f1x2 S 100,000 and g1x2 S 00 as x S…

A: Given information: The function f(x) approaches 100,000 and g(x) approaches infinity as x approaches…

Q: Determine the following limit: V1+ 4x – V1– 7x lim x →0

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…

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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.