Approaches
Definition
In calculus, "approaches" refers to the behavior of a function as the input values get closer and closer to a certain value or infinity. It describes how the output values of the function get arbitrarily close to a specific number or approach a particular limit.
Analogy
Imagine you are trying to hit a target with an arrow. As you shoot arrows from farther and farther away, your shots start getting closer and closer to hitting the bullseye. The arrows "approach" the center of the target.
Related terms
Limit: In calculus, "limit" is used to describe what value a function approaches as its input values get arbitrarily close to a certain point. It represents the behavior of a function near that point.
Converge: When we say that a sequence or series converges, it means that its terms approach a specific value or limit as more terms are added.
Diverge: On the other hand, when we say that a sequence or series diverges, it means that its terms do not approach any specific value or limit as more terms are added; they may grow infinitely large or oscillate between different values.
"Approaches" appears in:
Subjects (1)
Practice Questions (17)
What is the limit of the function f(x) = 3x^2 - 2x + 1 as x approaches 2?
What is the limit of the function f(x) = sin(x) / x as x approaches 0?
Consider a graph where the function f(x) approaches positive infinity as x approaches both positive and negative infinity. What can be concluded about the limit of f as x approaches infinity?
What can we conclude about the limit of f(x) as x approaches 3 based on the table?
Find the limit of the function f(x) = (3x^2 - 4x + 2) / (2x^2 - 5x + 3) as x approaches 1.
Find the limit of the function f(x)=(2x^2-5x+3)/(x-2) as x approaches 2.
What is the limit of (3x - 5)/(2x + 1) as x approaches -1?
What is the limit of (2x^2 + 5x - 3)/(3x^2 + 2x - 1) as x approaches 1?
What is the limit of (sin(x))/(x) as x approaches 0?
What is the limit of (e^x - 1)/(x) as x approaches 0?
What is the limit of (sin(2x))/(x) as x approaches 0?
What is the limit of (2^x - 1)/(x) as x approaches 0?
What is the limit of (3x^2 - 4)/(5x^2 + 2x) as x approaches -∞?
What is the limit of f(x) = (x^2 - 2x + 1)/(x^2 - 1) as x approaches 1?
What is the limit of f(x) = (e^x - 1)/x as x approaches 0?
What is the limit of the function m(x) = (x-2)/(x^2+4) as x approaches 2?
What is the limit of the function q(x) = sqrt(x) as x approaches 9?
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