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1. Consider the function whose formula is $f(x) = \frac{16 - x^4}{x^2 - 4}$? a. What is the domain of $f$? b. Use a table of values of $x$ approaching 2 to estimate the value of $\lim_{x \to 2} f(x)$, if you think the limit exists. And if you think the limit does not exist, explain why. c. Use algebra to simplify the expression $\frac{16 - x^4}{x^2 - 4}$ and hence work to evaluate $\lim_{x \to 2} f(x)$ exactly, if it exists. Or explain how your work shows the limit fails to exist. Discuss how your findings compare to your results in (b). d. True or false: $f(2) = -8$. Why?

          1. Consider the function whose formula is $f(x) = \frac{16 - x^4}{x^2 - 4}$?
a. What is the domain of $f$?
b. Use a table of values of $x$ approaching 2 to estimate the value of $\lim_{x \to 2} f(x)$, if you think the limit exists. And if you think the limit does not exist, explain why.
c. Use algebra to simplify the expression $\frac{16 - x^4}{x^2 - 4}$ and hence work to evaluate $\lim_{x \to 2} f(x)$ exactly, if it exists. Or explain how your work shows the limit fails to exist. Discuss how your findings compare to your results in (b).
d. True or false: $f(2) = -8$. Why?

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1. Consider the function whose formula is f(x) = (16 - x^4)/(x^2 - 4)?
a. What is the domain of f?
b. Use a table of values of x approaching 2 to estimate the value of limx → 2 f(x), if you think the limit exists. And if you think the limit does not exist, explain why.
c. Use algebra to simplify the expression (16 - x^4)/(x^2 - 4) and hence work to evaluate limx → 2 f(x) exactly, if it exists. Or explain how your work shows the limit fails to exist. Discuss how your findings compare to your results in (b).
d. True or false: f(2) = -8. Why?

Added by Marc B.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Kumareshwaran Rathinasabapathy

Step 1

The domain of f is the set of all real numbers r such that r - 4 is non-negative. This means that r must be greater than or equal to 4. So, the domain of f is [4, ∞). b. To estimate the value of lim f(x) as x approaches 2, we can create a table of values of f(x) Show more…

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Consider the function whose formula is f(r) = âˆš(r - 4). What is the domain of f? b. Use a table of values of x approaching 2 to estimate the value of lim f(x), if you think the limit exists. And if you think the limit does not exist, explain why. c. Use algebra to simplify the expression 1 / (x - 4), and hence work to evaluate lim f(r) exactly if it exists. Or explain how your work shows the limit fails to exist. Discuss how your findings compare to your results in (b). d. True or false: f(2) = 8. Why?

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