Question

Show that $\lim _{x \rightarrow 0}(-2 x+3)=3 .$ [Hint: Use Problem 54.]

   Show that $\lim _{x \rightarrow 0}(-2 x+3)=3 .$ [Hint: Use Problem 54.]

Calculus

Deborah… 5th Edition

Chapter 1, Problem 56

Instant Answer

Solved by Expert Carson Merrill

08/03/2021

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Step 1: We are given the function $f(x) = -2x + 3$ and we want to find $\lim _{x \rightarrow 0}(-2 x+3)$. Show more…

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Show that $\lim _{x \rightarrow 0}(-2 x+3)=3 .$ [Hint: Use Problem 54.]

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Key Concepts

Limit Laws

Limit laws are a set of rules that allow for the manipulation and evaluation of limits. These laws state that if the limits of individual functions exist, then the limit of their combination (such as sums, differences, and constant multiples) can be determined by combining their limits accordingly. This simplifies the process of evaluating complex limits.

Continuity

Continuity is a property of functions that ensures the function does not have any abrupt changes or breaks at a point. For continuous functions, the limit as x approaches a point is simply the value of the function at that point. Linear functions are a primary example of continuous functions.

Limits

Limits are a foundational concept in calculus which describe the behavior of a function as its input approaches a particular value. They help in understanding how functions behave near points where they might not be explicitly defined, and are essential for defining continuity, derivatives, and integrals.

Linear Functions

Linear functions, which are functions of the form f(x) = mx + b, are among the simplest types of functions in mathematics. They are continuous and differentiable everywhere, making the evaluation of limits straightforward through direct substitution. Their straightforward structure often serves as a gateway to understanding more complex functions in calculus.

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