Questions 1 and 2: Consider the graph of a function f(x). 1. (a) - S(x) (b) lim lim (c) (d) f(2) lim, f(x) (f) lim f(x) (e) lim f(x) (g) lim f(x) 2. (a) Is f(x) continuous at x = 2? Explain why or why not. (h) f(4) |(b) Is f(x) continuous at x = 4? Explain why or why not.

Q: 30. (а) f(-2) (b) lim f(x) 4 3+ (c) f(0) 2- (d) lim f(x) (e) f(2) -2 1 1 2 3 4 5 (f) lim f() -2- (g)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 3. Sketch the graph of a function y(x) with domain (-x, 0) that appears to satisfy each of the…

A: Given: The domain of the function is all real number,  limx→∞y(x)=5limx→-3y(x)=-∞limx→4y(x) does not…

Q: Question-1 Answer the following from the given graph: 10 a) lim f(x) X-2 8 b) lim f(x) c) f(0) d)…

A: from given graph it is clear that

Q: f (x )² – 1 When the function f(x) satisfies f(1) =1,f'(1)=3 obtain a value of lim x→1 - 1

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Q: 1. Consider the function f(, y) 2y (a) Show that lim (x,y) (0,0) f (x, y) does not exist by using…

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Q: What conclusion can be made if: a. A function changes from a decreasing interval to an increasing…

A: Given that: a. A function changes from a decreasing interval to an increasing interval.b.…

Q: 2² - 9 if x 0 3 (A) Find lim f(x) X→-3 (B) Find lim f(x) x→3 (C) Find lim f(x) (D) Find f(0) (E) Is…

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Q: 6- (a) lim f(x) x--2 (e) f(x) lim x-3- (b) lim f(x) X-2+ (f) lim f(x) lim, f(x) X3+ (c)

A: According to our terms and conditions I have solved first 3 parts for remaining part repost

Q: d. lim f(x) = x→-3/5 Preview e. lim f(x) = x→1 Preview f. lim f(x)

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Q: (a) A function is continuous from the left at a if (b) A function is continuous from the right at a…

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Q: [x², 7. a. Graph f(x) = l0, x = 1. b. Find lim,1- f(x) and lim,,1* f(x). c. Does lim,i f(x) exist?…

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Q: cos(x) - 1 For the function f(x) %3D (a) Compute lim f(x) =| (b) Compute lim f(x)=| (c) Compute lim…

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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: (-2x-1 ,xS-1 -11 a) Find the domain and range. c) Graph f(x) b) Evaluate : lim f(x) d) Determine…

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Q: Question: 3 3- 19-2x+ x² a. Evaluate lim X

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Q: Question 3: Let k > 0. VR? + 3x2 - k (a) Give A = lim (b) Sketch the graph of the function f(x) = (r…

A: A vertical asymptote is a vertical line that guides the graph of the function but is not part of it.…

Q: Sketch the graph of a function y = f(x) with all of the following properties. a. f'(x) > 0 for -9sx…

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Q: 1) lim r-3 x² – 3x x3 - Vx+4–1 2) lim x→-3 x+3 3) In the below graph (figure 1.1.2), figure 1.1.2 -2…

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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: limx→a+fx=fa

Q: 6 (a). Let f be a differentiable function with f(0) = 1, f'(0) = 2. f(x) + f(2x) + f(3x) - 3 Find…

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Q: Activity 2 1. Show that g(x) = x² + 1 is continuous at x = 1. a. g(x) b. lim g(x) X-1 c. Is the…

A: Given- gx=x2+1 To Show- That the above expression is continuous at x=1.

Q: 14. (a) Use a graph of 1(6) = (1- 2)" f(x) = to estimate the value of lim f (x) correct to two…

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Q: 1. 3 2 a) Find lim f(x), lim f(x) and lim f(x) b) Find f(1). c) Is f continuous at x = 1? Why or why…

A: We have given figure. And we have discuss about limit and continuity at some certain point.

Q: (%o +h) -f(%o) A continuous curve y = f(x) has a vertical tangent at x =x, if lim = 00 or - 0o. Does…

A: Continuity of function

Q: 1. Using the graph of f(x), what is lim, -f(x)? A. - 00 B. 0 C. -2 D. Does not exist E. 00 A

A: The graph of f(x) is represented by two infinite curves.

Q: In this exercise we investigate the curve et – 1 y = f(x) ez +1 (a) Explain why –1< f(x) < 1 for all…

A: According to our policy at Bartleby, I can solve only three sub- parts. Given a function :…

Q: 1 (b) lim [F(x) – g(x)] x-0 DNE (c) lim [f(x)g(x)] X--1 lim fx) x-3 g(x) 1 (d) (e) lim [x²F{x)] x-2…

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Q: 1) Sketch a graph of a function that has the following properties: lim f(x) = -2 lim, f(x) = 1 f(3)…

A: We can use the concept of graph in order to solve the given problem.

Q: 1. Sketch the graph of a function ƒ which has the following characteristics: f(0) = f(2) = f(4) = 0,…

A: The value of the function is 0 at the points 0,2,4 The slope of the function at 1 and 3 is 0 which…

Q: 4.3 #31| Sketch the graph of a function that satisfies all of the given conditions: f'(x) > 0 if x #…

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Q: -xx2 a) Find lim, + f(x), lim, 2-f(x) and/ (2). b) Dose lim, 2 f(x) exist, if so, what is it? If…

A: We need to find limit.

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: ·4 2. 3 a) Find lim g(x), lim g(x) and lim g(x) X+1 -2 x→1+ b) Find f(1). c) Is g continuous at x =…

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Q: lim f(x) # lim f(x). I c-

A: In question five, we to show  limx→c+f(x) not equal to limx→c-f(x) for monotonic function in (a , b)

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: 13. Sketch a graph of a function that satisfies all of the conditions given here. A vertical…

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Q: x 0 Can also be displayed as: f(x) = [x - 1 when x < 0, 1 when x = = 0, x² 1 when x ≥ 0] For this…

A: The given function,     fx=x-1,x&lt;01,x=0x2-1,x&gt;0

Q: 1-x if x 0 x+2

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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: Let ƒ(x) =

A: Given, The piecewise function is f(x)=3-x , x&lt;22       , x=2x2     , x&gt;2

Q: 4) (i) If lim f(x) = 18 and lim g(x) = 29 then find lim[2f()+ 6g(x)] x6 ( ii) Determine whether the…

A: Given : lim x→6g(x) =29  and  lim x→6f(x) =18  To find: lim [2x→6f(x) +6g(x)]   = lim 2x→6f(x)  +…

Q: 1 - x², 8. a. Graph f(x) = 12, b. Find lim,→l+ f(x) and lim,→1- f(x). c. Does lim,1 fx) exist? If…

A: Given function

Q: 10. Given the graph below, what is the value of x of the function H(x) is discontinuous? h(x)== A. 0…

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

Q: (5) Sketch the graph of a function y = f (x) that satisfies all of the following conditions. lim…

A: The graph of function satisfying given condition is as below

Q: 4 (a) Evaluate lim, 1 (-) (b) Let f(x) = ? – x. Find the value(s) of x if the second derivative f"…

A: Answer

Q: (x* - 2, ifx < 0 -2 , ifx 20 6. Given the piecewise function h(x) = Find a) lim h(x) b) lim h(x) *-…

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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.