What word or phrase best fits in the blank below? "If lim f(x) = L, then when x is near a the x → a corresponding values of f(x) are close _) to L." but slightly smaller when compared and possibly equal but never equal as they can be and always equal but slightly larger when compared

What word or phrase best fits in the blank below? "If lim f(x) = L, then when x is near a the x → a corresponding values of f(x) are close _) to L." but slightly smaller when compared and possibly equal but never equal as they can be and always equal but slightly larger when compared

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 8E

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Concept explainers

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.

Question

What word or phrase best fits in the blank below?
"If lim f(x) = L, then when x is near a the
x →a
corresponding values of f(x) are close
_) to L."
but slightly smaller when compared
and possibly equal
but never equal
| as they can be
and always equal
| but slightly larger when compared

Expert Solution

Step 1

To fill in the blanks.

If $\lim_{x \to a} f (x) = L$ , then when $x$ is near $a$ the corresponding values of $f (x)$ are close (_______________) to $L$ .

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