a. The number L is the limit of f(x) as x approaches c if given any ɛ > 0, there exists a value x for which |S (x)– L|< ɛ . b. The existence and value of lim f (x) never depends on what happens at x = a. c. If lim f (x)= lim f (x), then f is defined at x = 3. x+3 TX d. The function f (x) = tan 2 | has nonremovable discontinuities at x ="+tk , where k is an 2 integer. e. If r(x) is a radical function, then for any real number b in the domain of r(x), limr(x)=r(b).

Q: 1. Complete the following tables of values to investigate lim (x2 – 2x + 4). x→1 f(x) f(x) 1.6 0.5…

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Q: 4. Consider the following function. 5 – x x < -1 f (x) - 1<x< 5 (х — 5)2 x2 5 a. Sketch the graph of…

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Q: 6. Is it true that the limit of a function lim f(c) = L is the same as evaluating a function f(c)?

A: the limit of a function lim f(c) = L is the same as evaluating a function f(c)

Q: 5. lim x-0 e2x-1

A: LetL=limx→ 0xe2x-1Plug in the value x=0L=0e2(0)-1L=01-1L=00Therefore Apply L Hospital ruleL=limx→…

Q: Suppose that on the interval (2,5) f(x) less than or equal to g (x) less or equal to h (x) and Lim…

A: We have the following information.

Q: 1 Discuss the existence of the limit lim x 0 x2"

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Q: Find the value of the limit: 3x -9x e -e lim In(1+x)

A: Using limit to find the value of given function

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. - 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: Compute f(x +h) + f(x– h)- 2f(x) lim h-0 h2 for the following functions: (a) f(x) =x (b) f(x) = x2…

A: For the real function f, if f(a+h)-f(a)h has a limit, h approaches to zero. This limit is the…

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…

A:

Q: For the functionf(x) = |x – 2|, evaluate the left and right limits of f(x) as x approaches 2.…

A: We are asked to evaluate the limit.

Q: If a function is defined at a, but lim f(x) does not exist, how is x→a this shown on the function's…

A: If the limit of a function f(x) does not exist at a, then the function is not continuous at a and…

Q: find the limit of g(x) as x approaches the indicated value. lim (4g(x))'/³ = 2 X0+

A: Consider the given limit as limx→0+4gx13=2

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

A: To evaluate the below right-hand limit

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 function x^3+7x. Which one of the following limits represents f'(1) ? a. lim (f(1+h)as…

A: It is known that, if we have a function f(x) then the derivative of the function is defined as,…

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: 4. Do you agree with the following statement? When a function f is continuous at a number a, then it…

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Q: suppose f,g an d h are functions which g(x)<=f(x) <=h(x) ,for all x in an open interval containing a…

A: No. For the given continuous open interval domain, the limit of f(x) does not exist.

Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: The graph of a function f (x) is shown at right. If g(x) = v5 + 4x , find lim [f(x) + 3 g(x)]. А. 13…

A: Consider the given function: gx=5+4x Consider the given limit expression: limx→1+fx+3gx We can also…

Q: i. Calculate the following limit: 2x|x – 1| lim - x-1 x-1 ii. Determine the limit of f(x) when x…

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Q: Find the indicated limit given that lim f(x) = 2 and lim g(x) = 4. X→a lim [5f(x) – 4g(x)] Xa

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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: 1 Use a plot of f (x) = 4 Vx - 2 to estimate lim f(x) 4 メ→4 | numerically.

A: Given: f(x)=1x−2−4x−4Estimate:limx→4f(x)=?Graphically  and  Numericallly

Q: Use the e - 8 definition of the limit to establish a ô that proves lim (x – 1) = 2 x-2 O A) 3 B) 2e…

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Q: If a function f is not defined at x = a then the limit lim f(x) as x approaches a never exists.…

A: To check: Whether the statement is true or false: Given: The statement is " If a function is not…

Q: Suppose that f(x) = 1 if x 0. Does lim,→0 f(x) exist? (Draw a picture.) O No, because the limits…

A: Given, limx→0-=1limx→0+=2 Hence, limx→0fx does not exist  since both the limits are not the same.…

Q: If lim f(x) = +o, then f(a) is undefined. For those who have trouble viewing the Mathematical…

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Q: From the function H defined by sections a) Estimate the following limits: lim x→1/2h(x), lim…

A:

Q: From the graph: (x) is discontinuous at x= 3 because of (a) Lim f(x) = f(3) (b) Lim f(x) doesn't…

A: According to graph at x = 3

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

A: topic - limits

Q: Find the limit of the following, or show that it does not exist: lim (x,y) -&gt; (0,0)  (xy)/(x2+y4)…

A: By approaching (0,0) along the line y=x, we get

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: . What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

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Q: 3) Suppose that the limit of f(x) exists at z = 1 and let lim f(x) = 5. Find the following limits…

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Q: Find the indicated limit, if it exists. x+4 x<-5 lim f(x), f(x) = X-5 4 - x x2-5

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Q: 1. Prove, using the e-6 definition of limit, that: (a) (b) lim lim_2²+1=2 24-1 x³+x²+x+1= 4.

A: Limit

Q: Find the following limits when they exist:   1. lim g(x)   x to 3+

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Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→ ∞ x²

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Q: In some cases, numerical investigations can be misleading. Plot f (x) = cos π x . (a) Does lim x→0 f…

A: (a) Consider the function f(x). Plot the curve for f(x).

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: 6. Explain why the limits lim f(x+h) – f(x) and lim f(2) – f(x) h Z-X are each initially in the form…

A: Given that the limits are limh→0fx+h-fxh and limz→xfz-fxz-x.

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

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Q: Given that lim f(z)= 5 and lim g(1) =-1, evaluate the following. Eナー1 %3D N-1 lim (f(x) · g(z)) エ→ー1…

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Q: Suppose that lim, →o(f(x) – 9(x)) = 0 and h(x) is a function with domain R. a) Assume that |h(x) –…

A: We will answer the first question as we only answer one question at a time. Please resubmit the…

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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