..... a) lim f(x) x→5 b) lim f(x) x→5* c) lim f(x) x-5 d) f(5) = e) C. The function is continuous at x = 5 D. The function is discontinuous at x = 5 as there is an asympotote there .....

Q: 2. By drawing a graph illustrate an example of a function f(x) such that it satisfies these three…

A: Topic = Functions

Q: Let a be and integer and b be a nonzero integer. Prove that alb if and only if Mb C Ma.

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Q: Let f(z) 2 = = (-)². Show that lim f(z) does not exist. z➡0

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Q: Suppose f: (0, ∞o) → (0, ∞o) is a continuous function. True or false: lim √f(x) = = /lim f(x). 2-5…

A: We have to find whether given statement is true or not?

Q: 1. Using the limit rules, find lim f(x) for the following functions: (a) f(x)= 3. (b) f(x)=¿e-2*.…

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Q: 6- Follow the graphing strategy and analyze the function f(x)= 3x³ -10x³ State all the pertinent…

A: We have to graph the given function and also find the limits.

Q: Which of the following statement/s is/are true about the function whose graph is shown below? A fx)…

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Q: 1. Complete the following based on the graph of f(x). 0 10-8-6-4-2 CO 6 4 2 2 -4 क -8. f(x) e 246 6…

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Q: Sx² 15 a. Find lim f(x). if x + 2 2. Let f(x) = } if x = 2 X→2 b. Find f(2). Is f(x) continuous at x…

A: Proceed as shown below...

Q: . Let (x2 + 1 f(x) = 1( - 2)² if x> 1 if x<1 (a) Find lim,-I- f(x) and lim,→* f(x). (b) Does lim ,1…

A: Given: For (a),     limx→1- f(x)=limx→1 x2+1=12+1=2 and     limx→1+ f(x)=limx→1 x-22=(-1)2 =1

Q: Find the limit

A: The given expression limx→013+x-13x

Q: . The function f (x) is defined by the rule 2-36 if x + 6 f (x) x-6 25 if x = 6 (a) Calculate lim f…

A: Continuity criteria :  f ( x ) is continuous at x = a when following properties are satisfied :  1)…

Q: Estimate the value of limx→2 x 2 + x − 6 x 3 − 8 to 3 decimal places by making a table with the…

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Q: Give an example of a function that is not continuous at x = 2 but limx→2 f(x) = 1

A: choose any equation of line such that f(2)=1 but the function function f(x) should be discontinued…

Q: If lim f(x) = 4, what can you say about ƒ(1)? x-1

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Q: 3. If f is a continuous function, what can you say about lim f(x)?

A: Given thatf is continuous To determinelimx→1f(x)

Q: (-1)* 3k 6k3+1 14. Determine how many terms of the convergent series k=1 the remainder is less than…

A: Consider the given convergent series, ∑k=1∞-1k3k6k3+1 so, ak=3k6k3+1 Here we have given that…

Q: 13. Sketch the graph of f (x) = }" Sx² + 1 if x -1 and use it to evaluate lim_ ƒ (x) and X→-1- lim…

A: Given that: f(x)=x2+1    if    x≤-13            if     x&gt;-1

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: 1 (B). Evaluate lim (3 – x) x-2 x→2

A: Given that  lim x to 2 (3-x)^(1/(x-2))

Q: Find the following (if they exist) for the function whose graph is given below:

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Q: If lim f( x ) + f(a) ,then f(x) is at continuous , y = f(a) not continuous ,x = a continuous, x = a…

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Q: x²-4 lim x-2 (x-2)² 2–4

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Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

A: The graph of the function g(x) is shown as,Since parts a to c are already solved in original…

Q: Which of the following statement/s is/are true about the function whose graph is shown below? fix)…

A: Given the graph of the function f(x). To find which of the following option is/are  correct.

Q: 3. Sketch a graph of a function (x) for w ich all of the fo lowing are true: lim-2' f(x) = -4,…

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Q: Consider the following graph of the function f. X-0 lim f(x) = X→0+ -3 -2 -1 4 3+ True False 2 - + 2…

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Q: Sketch a graph of a function that satisfies all of the following properties. -4- a) f(-6) is…

A: We need to sketch the graph.

Q: a. What is the domain of f? Express your answer in interval notation. f(x)= 1 - x^4 / x^2 - 1  b.…

A: The given function fx=1-x4x2-1. We have to find the domain, limit at x=1 and sketch its graph.