1³ +2, if r < 0 if r > 0 Suppose f(r) = ||r – 2|, (a) Find lim f(x). (b) Give a simple reason why f is discontinuous at 0. (a) Suppose f is a function with domain [a, b]. If ƒ is an odd function, what can be deduced about a and b? (b) Give an example of an even function whose domain has exactly five elements.

Q: The graph of the function f(x)=secx is given above for the interval x∈[0,2π] ONLY. Determine the…

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Q: Sketch the graph of the function defined piecewise by the formula f(x) = {0, x ≤ −1 ; √1 − x^2 , −1…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: x+2 Q1I) If f(x) =* and h(x) = v2 –x, 3-x find (1) (f o h)(x) (2) Domain and Range for all f (x),…

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Q: Consider the function f that is defined over R - {-1} as: ƒ (x )=- x²-2x +1° Designate by (C) its…

A: 1) limx→1x2x2-2x+1=limx→1x2(x-1)2=∞ Therefore, x=1 is the verticle asymptotes. 2)…

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: 1. Find the intervals on which f (x) = Vx² – 9 is continuous. 2x 2. Either find lim ( -) or use a…

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Q: (a) Estimate the value of lim 1-0 V1 + 3x – 1 by graphing the function f(x) = x/(/T + 3x – 1). (b)…

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Q: The process by which we determine limits of rational functions applies equally well to ratios…

A: The given limit expression is limx→ -∞ 1-x3x2+7x5.

Q: Show that the function f(x) = |x - 3| is not differentiable at 3. We have x- 3 if x 2 3 f(x) = |x -…

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Q: Show that the function f(x) = |x - 2| is not differentiable at 2. We have if x 2 2 f(x) = |x - 21 =…

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

A: Substitute x= 5 in the function and find the limit

Q: 1. Determine whether the function f(x) = x2 + 6x + 9 is continuous at x =-= Sketch its graph…

A: Consider the provided function and the point, fx=x2+6x+9,   x=-2 Evaluate the provided function at…

Q: 1) The graph of a function y = f(x) has the line y = -2x + 5 as its tangent at the point (3, 10).…

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Q: 1. Decide whether the function f(r) = admits any horizontal asymptotes, i.e. compute lim f(x) = Give…

A: (1). The function is given by f(x) = xx+4 To evaluate : The horizontal asymptote.

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: Choose the best answer for limit.

A: limx→2-f(x)=limx→2-f(x)=-1 , f(2)=1we have to find limx→2f(x)

Q: Create an example of a function f, such that f(3) and lim f(x) are both defined and yet have…

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Q: (6) Let f be a function with domain R. Suppose that lim f(x) = 7. Prove, directly from the ɛ – ô…

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Q: x°- a Calculate the limit lim using the following factorization formula where n is a positive…

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Q: Show that the function f(x) = |x – 2| is not differentiable at 2. We have if x > 2 f(x) = |x – 2| =…

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

A: Let's find.

Q: Show that the function f(x) = |x – 4| is not differentiable at 4. We have if x 2 4 f(x) = |x – 4| =…

A: givenf(x)=x-4right hand limitlimx→4+f(x)-f(4)x-4=limh→04+h-4-4-44+h-4=limh→0hh=limh→0hh=1left hand…

Q: 1. Sketch the graph of a function f that satisfies all the following conditions. The domain is (-4,…

A: Given that the domain of the graph is (-4,∞) limx-&gt;-4+f(x)=3 when x approaches from the right of…

Q: (a) Estimate the value of lim X - -00 (V x2 + x + 7 + x by graphing the function f(x) = V x2 + x + 7…

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Q: 2. a. Evaluate lim f(x) , where f(x) = {Nx+ (M +77) if x <5 IN-px if x 25 P" is any constant and…

A: Limit exist if Right hand limit and left hand limit are equal. Note : According to Bartleby…

Q: 5-Vx 4) lim x-25 x-25 5) lim 7-x ל-x ( x² – x3 if x <2 6) Given the function g(x) 15x – 14 if x 2 2…

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Q: 4. Use the given information to sketch the graph of the function f. (-2,1)u(1,x) all real except X -…

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Q: 1. Sketch the graph of a function with the given properties. lim f(x) = 2, lim f(x) = -, lim f(x) =…

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Q: What conclusion about f(x) can be drawn from the equation lim,-a* f(x) = f(a)? A. It is a continuous…

A: What conclusion is correct about fx if limx→a+fx=fa. A. A function is continuous at a number a if…

Q: True or False: If lim f(x) = infinity as x-->2, then the graph of f has a horizontal asymptote at…

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Q: x2 - 16 - if x>0 x + 4 2) Let f(x) = %3D x2 - 16 - if x<0 X- 4 Find lim f(x). x-0-

A: First I have written the definition of left hand limit , just use this definition for given function…

Q: Hon of the Squeeze Theorem) on the same screen. 37. If 4x-9 ((x) x* - 4x + 7 for x> 0, find lim f(x

A: Given: If 4x-9≤f(x)≤x2-4x+7 for x≥0. find limx→4f(x)

Q: 1. Given 2-x 06 a) Do the following limits exists at lim f(x) and lim f(x). b) Does function f…

A: We have to solve the limits.

Q: 2.4.13 f(x) Suppose f(x)→- 150 and g(x)→0 with g(x) <0 as x-3. Determine lim X--3 9(x) 1(x) lim…

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Q: 1. Consider the given piecewise function f(x), find the limits at the given values. State if the…

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Q: Question #1) Use the graph of the function to determine the indicated limit -12 -10 -8 -6 4 -2 10 12…

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Q: 1/(1+e^(1/x)) state the value of each limit. lim f(x) as x -> 0- lim f(x) as x ->0+ lim f(x) as x…

A: Given:  f(x)=11+e1/x

Q: 1-x if x 0 x+2

A:

Q: A function is a ratio of quadratic functions and has a verticalasymptote x =4  and just one…

A: Given: A function is a ratio of quadratic functions. Vertical asymptote at x =4. x -intercept: x =1…

Q: if the line x=0 is a vertical asymptote of y=f(x) then the function is not defined at x=0 true or…

A: Asymptote is a straight line that continually approaches a given curve but does not meet it at any…

Q: Show that the function f(x) = |x – 3| is not differentiable at 3. We have if x 2 3 (x) = |x - 31 =…

A: Now, lim x→ 3+fx-f3x-3=limx→3+x-3-0x-3=1lim x→ 3-fx-f3x-3=limx→3--x-3-0x-3=-1

Q: 1. (a) Find the interval in which conditions of Rolle's theorem are satisfied for the function f(x)…

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Q: 1. (a) Evaluate the limit or state that it does not exist: i. lim 32-1 37-1 ii. lim V1+r-VI-x (b)…

A: The limits are required to be solved. Each part is solved in detail below.

Q: 2*+2, for x 2, Choose the correct answer below. O A. The given function is continuous at x = 2…

A: The function y = f(x) is continuous at point x = a if the following three conditions are satisfied.

Q: Q.No 3.) if x<-1 Let f(x)={ax+ B if -13x<1 x² +2 if x21 Find a and B, so that lim f(x) and lim f…

A: Given that, Consider, limx→-1-f(x) = limx→-1- x3 = (-1)3 = -1 limx→-1+f(x) = limx→-1+ (αx+β)=…

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: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

A:

Q: 3. A critical number for a function does not have to be in the domain of the e 4. The x-value of a…

A: 3. True 4. True 5. False 6. True

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.