12 – r|, 2. Suppose f(r) = {0, if a > 2 if r = 2 14 – 22|, if r < 2. (a) Find lim f (x). z+2+ (b) Find lim f(r). (c) State the value of lim f(x) and the precise reason. (d) State the precise reason why f is continuous at 2.2

Q: Consider the function f(x)=(x4 -2x3)/(x-2). Verify that Lim (x->2) f(x)=8. In order to guarantee…

A: Consider the function f(x)=(x4 -2x3)/(x-2). To Verify that limx→2f(x) = 8

Q: If 3x - 4 s f(x) sx2 - 3x + 5 for x 2 0, find lim f(x). x-3

A: Given, 3x-4 ≤ fx ≤ x2-3x+5              for  x ≥ 0 We have to find limx→3fx

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: If 3x < f(x) < x³ + 2 for 0 < x < 2, find lim f(x). x-1

A:

Q: If a function f has no limit as x approaches c, then we say that lim f(x)

A:

Q: f(2 + h) – f(2) Find lim if f(x) = x + 7. h h→0 f(2 + h) – f(2) lim | (Simplify your answer.) h h→0

A: Here I am attaching image so that you understand each and every step.

Q: Use the graph of the function f shown below to respond to each prompt. The first prompt is worth 3…

A:

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: 2x 1 if x 2 . Sketch the graph of f(x) = x 4. a) lim f(x) X-2 b) lim f(x) x-2+ c) lim f(x) X-2

A:

Q: Use the graph of f(x) below to answer the following questions: 4 3 2 y y=f(x) 1 1

A:

Q: Consider the following graph of the function g. From the given graph of g, state the numbers at…

A: The graph of a function g is given, to find its points of discontinuity.

Q: If 2x – 2 < f(x) < x² – 2x + 2 for x 2 0, find lim f(x). X-2

A: The objective is to find the limit.

Q: Suppose a function f satisfies f(3+h) – 2 lim = 7. Find an equation for the line tangent to the…

A: Let

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: 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 f is a function such that f(2)=4,can you conclude anything about lim as x tends to 2 for the…

A: The objective of the question is to understand if we can conclude anything about the limit of a…

Q: f (x) =  x^2 +2         x3         1. At what value is this function discontinuous, if any?…

A: Given function, f(x)=x2+2,     x&lt;310     ,      x=3-3+4x,   x&gt;3

Q: Use the 8 and € approach like we did in our class to prove the following lim (3x²-5) = -2, Assume 8…

A: