The limit of a function if x approaches some value, a, exists if: a. the function is of the form f(x) = xⁿ where n is a rational number b. two of the other answers are correct c. the function is a polyomial function with NO domain restrictions  d. the same value of 'f' is converged upon as x approaches a from both sides of a

Q: Determine the values of a where the function f (x) is not continuous. Label each discontinuity as…

A: Given function is continous for all real values of x.  As per given instructions,  Enter NA in both…

Q: Determine the values of a where the function f (a) is not continuous. Label each discontinuity as…

A:

Q: A small island is 5 miles from the nearest point P on the straight shoreline of a large lake. If a…

A: From the given data, The scenario of this trip is described as in figure below:     Let,  x be the…

Q: Determine the point at which the function f(x) = = '? Removable Jump Infinite None of these 1.…

A: We can find where the function is discontinuous.

Q: Find the long run behavior of each of the following functions. If the function goes to xo or -∞o…

A:

Q: What type of discontinuity occurs at x = 1 for the piecewise function? if x <1 if 1<x 3+ x h(x) =…

A:

Q: inimum value of - 6x - x². 9 5.abs

A:

Q: (5) State the value(s) of x where the functions are discontinuous (x = a) AND the type qf…

A: Given that, fx=1               if x&lt;2x+3         if 2≤x≤47              if x&gt;4

Q: Suppose that a function f is analytic on the interval (1, 10). Suppose that another function g is…

A: Given  Suppose that a function f is analytic on the interval (1, 10). Suppose that another function…

Q: 3- Find the value of k So that the function f is continuous at the indicated point: (kx², if x 2…

A:

Q: aph each piecewise

A: d) Given,            f(x)=x+2,if x≤-1-x2+2,if x&gt;-1

Q: Consider the following piecewise function: Find the values of the constants C and K that will make…

A: We have to find value of C &amp; K

Q: Find the absolute minimums and maximums of the following function on the given intervals

A:

Q: x + a x+b It will be decreasing all throughout its domain if b> a. It will be increasing for x- b.…

A: Given function: fx=x+ax+b

Q: Is the following function continuous? x2 – 9 if x 3 if x = 3

A: The function is given by

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.