Creating functions satisfying given limit conditions Find a function f satisfying lim - f1x2 2. xS1x - 1

Q: LIMITS of a FUNCTION Evaluate the followinci limits. 2-Vx 3. lim, 4-x x - cos X 4. lim,

A: 3. To evaluate the limit limx→42-x4-x Solution We know that a2-b2=a+ba-b. Evaluating the limit.…

Q: sin(3x) Evaluate the limit : lim Show x→0 2x + x3 your work.

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Q: 5. lim f(x) = +, lim f(x) = 0 and f(-1) = 0 6. lim f(x) = +, lim f(x) = 0 X-1- x- 1+ x- 1+ and f(-1)…

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Q: Xー4 1. lim X-4 x2-3x-4 3.9 3.99 3.999 4 4.001 4.01 4.1 f(x)

A: It is given that

Q: Discuss the continuity of the function on the closed interval. Function Interval 6 - x, f(x) = 6 +…

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Q: 1 Estimating Limits Numerically Complete the table of values (to five decimal places), and use the…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re…

Q: Explain why or why not Determine whether the followingstatements are true and give an explanation or…

A: Since you have asked multiple questions in a single request we will  be answering only the first…

Q: LIMITS lim f(x) ахт + ... lim x→0 bx" +... X00 х3 — 2х2 + 3х — 4 lim х3 — 2х2 + 3х — 4 lim х-00 4x3…

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Q: lim f(x) Find x-2 lim f(x) and x-2*

A: We have given the graph. now using it we have to find left hand limit and right hand limit at x=2.

Q: Existence of a Limit Determine whether lim f(x) exists. Explain. lim f(x) = 1 and lim f(x) = 1 x→3-…

A: Consider the given limits limx→3-fx=1 and limx→3+fx=1   Limit of fx at any value of x, say x=c…

Q: Determining limits analytically Determine the following limits. 1 1 a. lim S2 Vx1x – 22 b. lim xS2…

A: (a) To find the limit as x approaches 2+ means, x approaches 2 from the right side or x - 2 >0…

Q: Uniqueness of limits Show that a function cannot have two differentlimits at the same point. That…

A: Suppose fx:K→ℝ and c∈ℝ is a limit point of K⊂ℝ.Assume limx→cfx=L1limx→cfx=L2Where L1, L2∈ℝ

Q: х-2 6. lim x-2-2-V4x-x2

A: The objective is to find value of expression, limx→2-x-22-4x-x2

Q: Sex if x 1 Find the left-hand and right-hand limits at the given value of a. lim f(x) x-1 lim f(x)…

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Q: (x^3-x^2) divided by (x-1) lim x-> 1 Evaluate the limit.

A: GIVEN: limx→1 x3 - x2x - 1

Q: Domain: x* lim f(x) = x3 lim f(x)= x-3- lim f(x) x-3+ lim f(x) = f(0) = f(x) = 0= x3D}

A: (a) From the given graph of f(x), When x approaches 3 from the left and from the right, y approaches…

Q: lim F(x) x--2 Select the correct choice below and fill in any answer boxes in your choice. OA. lim…

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Q: One-sided limits a. Evaluate lim Vx - 2. xS2+ b. Explain why lim Vx - 2 does not exist. xS2-

A: We know that a function fx=x is defined if x≥0. a. We have to evaluate limx→2+x-2 Here x→2+ it means…

Q: able of values to estimate the value of the limit (correct to three decimal places). If you have a…

A: Please refer to the image below

Q: Determining limits analytically Determine the following limits. x - 3 x² - 5x + 4 x - 3 a. lim xS1…

A: given, limx→1+=x-3x2-5x+4limx→1-=x-3x2-5x+4limx→1=x-3x2-5x+4

Q: thèy exist. If the limit does not exist, explain why. 51 3 7 lim f(x) lim f(x) lim f(x) I-00 lim…

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Q: lim i If X -C lim 6 f(x)g(x) exists then both lim ¿ lim & g(x) exist, regardless of X -C X -C the…

A: Let us denote f(x)=5 if x<215 if x≥2g(x)=15 if x<25 if x≥2Then limx→2f(x)=does not exist and…

Q: 1 17. lim - x-3 (x-3):

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 11-16 · Estimating Limits Numerically and Graphically Use a table of values to estimate the value of…

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Q: x*+x-2 Evaluate lim or state that the limit does not exist. If the limit does not exist, -i…

A: Given: limx→1 x3+x-2x3-x2-x+1  To find: The given limit and the one sided limits.

Q: *The limit of a function Evaluate the given limits numerically (using table of values) and…

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Q: Limits of composite functions Evaluate each limit and justify your answer

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Q: lim [x2 . (1 – cos x)] = x→0 1 1 The limit does not exist. 8.

A: Using rules of Limit.

Q: Estimating a Limit Consider the function x + 1| - |x – 1| f(x) = Estimate |x + 1| – |x – 1| lim -…

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Q: Determining limits analytically Determine the following limits. x - 1 lim xS2 V1x – 321x – 22

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

Q: tex ex lim 3. 2x°+x² +3x -4

A: we have to find limit

Q: Test II: Evaluate lim 7*+h)-/ for the given function f (show f(x+h)-f(x) h→0 solutions) 2. f(x)=…

A: we can find limh→0f(x+h)-f(x)h for given f(x).

Q: x3 + x2 – x – 1 The value of lim -is the same as x- -1 x3 - 3x-2 X- 1 lim A X+ -1 X-2 X- 2 lim B X+…

A: Using l hospitale rule

Q: Discuss the continuity of the function on the closed interval. Function Interval 1- x, f(x) = { 1 1…

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Q: Determining limits analytically Determine the following limits. lim csc x xS0-

A: we have the limit limx→0-cscx

Q: lim x to infinity x-2/x2+1 find the limit

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Q: 2x-1)^5 divided by (3x^2+2x-7)(x^3-9x) lim x -> infinity   Evaluate the limit.

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Q: x-2 Use limits to determine if f (x) = is continuous at x = 1. x2-4 Yes, it is continuous because…

A: Use limits yo determine if f(x) = (x-2)/(x2-4) is continuous at x=1.

Q: y Prove that the limit does not exist. EXAMPLE 8 lim Ix - 3| х > з х-— 3 SOLUTION ]x – 3| lim lim X-…

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Q: LIMITS of a FUNCTION Evaluate the followina limits. - 4| 1. lim, X- 2

A: Let,f(x)=limx→2x2-4x-2Put,x=2 ,=limx→222-42-2then, the limits take 00 formNow,using L-hospital…

Q: Finding the Limits Based on Graph Find the limits of the function as given in the graph: lim f(x) 1.…

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

Q: [1/(x+1)]-1 The value of lim -is the same as X+0 A - lim[(x – 1)] X+0 (B) lim [(x + 1)] X+0 1 - lim…

A: The objective of the question is equating the given limit of the function.

Q: x - 2 lim find lim 9 (x) + a. Let g (x) = t. 9 (x). lim find lim h (x)- 17 + 2x Let h (x) = b. x -…

A: a) gx=x2+x-2x2-xb) hx=17+2xx2-2x+1

Q: Limits of functions Evaluate the following limits.

A: Definition used-             Limit of the function of two variables-…

Q: lim + x (Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE…

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Q: lim f(x) = x→6.2+ lim f(x) = x→6.2¬ At the point x = 6.2, the function is %3D right-continuous only.…

A: The function is,   The limit of function f(x) from the right of 6.2 is,

Q: sketch the graph of a function with the given limits.

A: It is given that lim fxx→1+=∞ lim fxx→1-=3limx→4fx=-∞

Q: 3. lim f(x) = -2, X-2 4. X-3 lim f(x) = +00, lim f(x) = 2 and f(2) = 0 lim f(x) X-3* %3D = -00

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Q: 8 Given a function: f(x) (х-7)(х-1) Write down the definition that lim f (x) = L X→a = -1| 8 Prove…

A: We have to prove the given condition