Consider the function 22 -6x+8 f(2) = x-2 if a + 2 if æ = 2. a We want to define a such that the function f is continuous for all e. a) The definition of the function f for a #2 can be simplified. After simplication, we have f(x) = for æ + 2. b) Compute the following limit. lim f(x) = c) For which value of a do we have that f is continuous for all æ? Answer: a =

Q: Question 8 If f(x) is a constant function. Then for any real number a f(a + h) – f(a) lim h 0 =0. h…

A:

Q: If g is a function such that (x+ 1)? 2 g(x) > 3(2r – 1) for all r > 0. Determine lim g(x).

A:

Q: 3 Use the Squeeze Theorem to evaluate lim f(x), where f(x)=x²cos (-). x A B C D - 0 0 1 8 -0-x

A:

Q: 2X + 3. lim x→2 X –3 f(x) f(x)

A: Given function f(x)=2x+1x-3we can can find the values around 2 to find the limit at x=2

Q: values

A: We will find the limits.

Q: f(x + h) – f(x) Evaluate lim h-0 for the given value of x and function f h f(x) = 5x2, x = -2 f(x)…

A:

Q: The graph below is the function f(z) -4 -3 -2 J -2 -4- Determine which one of the following rules…

A:

Q: The graph below is the function f(1) 4. -5 -4 -3 2 -2+ Determine the following values. Enter "DNE"…

A:

Q: Decide whether the limit exists. If it exists, find its value. Find lim f(x) and lim f(x). x-(-1)…

A: Topic = Limits Correct option = B

Q: The graph below is the function f(x) 16 O N -5-4-3-2-1 -2 -4 -54 Determine which one of the…

A:

Q: Consider the function below. Use it to evaluate each of the following expressions. (If an expression…

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.…

A:

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: Suppose that f is a function such that lim-[f(x) - 2x²]= π. Determine, if possible, lim 118 x² +1'

A: Suppose that f is a function such that, limx→∞fx-2x2=π.  To determine, limx→∞ fxx2+1, if possible.

Q: 8. Answer all of the questions below about the function f(x) graphed below when x = -4. Write dne…

A:

Q: Give the three conditions that must be satisfied by a function to be continuous at a point. Select…

A: For a function to be continuous at a given point,it should be defined at that point and its limit…

Q: Let g(x) be the following piecewise-defined function: 9 – x2 if x + -3 g(x) = 2(x+3) B2 if r = -3…

A:

Q: We know the following limit expression to be true: lim (-x² + 8x-6) = 1 X-1 Choose the most direct…

A: The limit of the function f(x)= (-x2+8x-6); is 1 when x tends 1 .

Q: The graph of the function f is shown in the figure. Which of the following statements about f is…

A: Explanation of the answer is as follows

Q: Let f be a function defined by f (x) : S4 – x?, x + -3 1. Evaluate l1, x = -3 а. ズ→ー3+ lim f(x) b.…

A: To find out the limits.