if x< 12 f(x) = 11 if 12 Sx< 65 8 if x2 65 The function shown represents the cost, f(x), in dollars, of a ticket at a movie theater in terms of the age, x, in years, of the person seeking admission. Which of the following is true about the limit lim f(x)? x12 O The limit exists and is equal to 6. O The limit exists and is equal to 8. O The limit exists and is equal to 11. The limit does not exist.

Q: 1. Let f and g be the functions with the graphs given below. Evaluate the following limits: • lim g…

A:

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

A:

Q: 3

A: Step 1: Step 2: Step 3: Step 4:

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

A:

Q: d. lim f(x) e. lim f(x) f. lim f(x) X-4 X4+ X-4 10- 8- 6- 4- 2- X in Click to select and enter your…

A: Please see the explanation below

Q: 4. Sketch a function f such that: lim f(x) and f(4) exist and are equal to one another. x→4 5.…

A:

Q: lim f (x) X-4 3.9 3.99 3.999 4 4.001 4.01 4.1 f(x) 7.9 7.99 7.999 8.001 8.01 8.1

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: