Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. f(x) = x+√√√x-9, For a 9, we have lim f(x) lim (x+√√x-9) x-a x-a = lim (x) + lim = x-a x-a lim (x) + V x-a = lim (x) + x-a lim x-a lim x-a [9,00) by the sum law by the root law lim (9) by the difference law x-a = = - 9 by the direct substitution property Therefore, f is continuous at x = a for every a in (9, 0). Also, lim¸ f(x) = x-9- = f(9), so f is continuous from the right at 9. Thus, f is continuous on [9,∞).

Q: lim2

A: Explained below

Q: Use a graph to explain the meaning

A: Given: limx→af(x)=∞For instance:Let us consider the function to be f(x)=1x2then  limx→0f(x)=∞

Q: 2x+12 |x+6| If f(x)=- , determine whether lim f(x) exists. 44-6

A:

Q: Find the limitsof: lim 34 メ+34 -V34 メしe

A:

Q: For the function f(x) shown below, determine lim f(x). f(x) = x² - 10 -3 - 2x for for +-←æ x -4

A:

Q: If lim x-4 x-2 f(x)-5 - =1, find lim f(x) X-4

A:

Q: when at x=a, f(a) is a real number. The function assumes an indeterminate form when x=a, both the…

A: 1) this is true. 2) this is also a True.

Q: Use a table of values to evaluate the limits of the given function

A: Let's find.

Q: Evaluate lim x → 5 x²-3x - 10 x-5 Enter an exact value below.

A: Given;  Limx-5(x2-3x-10) /(x-5).

Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

A: