Consider the function f (x) is continuous at a, which of the following is NOT true and O f(a) is defined (a is in the domain of f) lim f (x) exists lim f (x) =a All of the above are true

Q: f(a) exists lim, a f(x) exists the two above values are equal: f(a) = limr→a ƒ(x) x²–4x+3 if x 3…

A: Topic -Limit and continuity

Q: (4) Let f(x) be the function whose domain is all of R given by the rule 42 if r € Z and f(x) = 10…

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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: values

A: We will find the limits.

Q: If f(x+ y)= f(x)f (y) for all x, y eR and f (x)=1+g(x)G(x), where lim g (x)=0 and lim G (x)…

A: The problem has been solved in detail in the next step.

Q: 6. Consider a function f with the following property: if g is any function for which lim g(x) does…

A: One side is not true i have given the contradiction.

Q: If a function f(x) is given by x²-2x-8 T²-7x+12' 6, is f(x) continuous at x = 4? = x 4, x = 4, Yes…

A: The given function fx=x2-2x-8x2-7x+12,x≠46,x=4. We have to check whether the function is continuous…

Q: Define a function f(x) such that all of the following conditions are satisfied: • The domain of f is…

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Q: Let f(x) be defined on an interval (a,b) and suppose that f(c) #0 at some c where f(x) is…

A: 1)Therefore correct option is4) All of the above

Q: USE SQUEEZE Theorem do poho Lim I'm x² esin(x) и х 0+X

A:

Q: x→4 5. Sketch a function f such that: lim f(x), lim f(x), and f(4) all exist, but no two are equal.…

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Q: is differentiable at iff exists. lim h→0 f (x) True a [For your information: "iff" is an…

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Q: Let f be entire and suppose that lim 80+z f(z) Z = 0. Show that f is constant.

A: The given problem is to show that if limz→∞f(z)/z = 0 for the entire function f(z), then f(z) is…

Q: Evaluate f(a), lim f(x), lim f(x), lim f(x). Is f(x) continuous at x = a. x→a- x→a+ xa if x 4

A: For 4^- we use the first piece of the function

Q: If f: Z → R is a function, then the expression lim f(x) is undefined. x-2 True False

A: If f:ℤ→ℝ, is a function then  limx→2f(x) is undefined. To Check: Whether the given statement is true…

Q: -10 69°F 5 10 5 O -5 -10 Evaluate lim f(x), lim f(x), and lim f(x). X→ -6 x → - 2 X→ 4 5 10

A: We are going to solve

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: 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: If f(x) = 2x? – x + 2 , what is lim 2x2 – x + 2, lim 2x2 – x + 2, andf(2)? Is f(x)continuous at 2? O…

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Q: 3. Sketch the graph of a function f such that the following conditions are true: ● f(4) is not…

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