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- https://math.libretexts.org/Courses/Butler_Community_College/MA148%3A_Calculus_with_Applications_-_Butler_CC/02%3A_The_Derivative/2.02%3A_Limits_and_ContinuityIf the values of \(f(x)\) get closer and closer, as close as we want, to one number \(L\) as we take values of \(x\) very close to (but not equal to) a number \(c\), then we say "the limit of \(f(x)\)...If the values of \(f(x)\) get closer and closer, as close as we want, to one number \(L\) as we take values of \(x\) very close to (but not equal to) a number \(c\), then we say "the limit of \(f(x)\) as \(x\) approaches \(c\) is \(L\)" and we write \[\lim\limits_{x\to c} f(x)=\mathbf{L}.\nonumber \] The symbol "\( \to \)" means "approaches" or, less formally, "gets very close to".
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2160%3A_Applied_Calculus_I/01%3A_The_Derivative/1.02%3A_Limits_and_ContinuityIn the last section, we saw that as the interval over which we calculated got smaller, the secant slopes approached the tangent slope. The limit gives us better language with which to discuss the idea...In the last section, we saw that as the interval over which we calculated got smaller, the secant slopes approached the tangent slope. The limit gives us better language with which to discuss the idea of “approaches.” The limit of a function describes the behavior of the function when the variable is near, but does not equal, a specified number.
- https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/MATH_110%3A_Techniques_of_Calculus_I_(Gaydos)/02%3A_The_Derivative/2.01%3A_Limits_and_ContinuityIn the last section, we saw that as the interval over which we calculated got smaller, the secant slopes approached the tangent slope. The limit gives us better language with which to discuss the idea...In the last section, we saw that as the interval over which we calculated got smaller, the secant slopes approached the tangent slope. The limit gives us better language with which to discuss the idea of “approaches.” The limit of a function describes the behavior of the function when the variable is near, but does not equal, a specified number.
- https://math.libretexts.org/Courses/Chabot_College/MTH_15%3A_Applied_Calculus_I/02%3A_Limits/2.01%3A_LimitsIf the values of \(f(x)\) get closer and closer, as close as we want, to one number \(L\) as we take values of \(x\) very close to (but not equal to) a number \(c\), then we say "the limit of \(f(x)\)...If the values of \(f(x)\) get closer and closer, as close as we want, to one number \(L\) as we take values of \(x\) very close to (but not equal to) a number \(c\), then we say "the limit of \(f(x)\) as \(x\) approaches \(c\) is \(L\)" and we write \[\lim\limits_{x\to c} f(x)=\mathbf{L}.\nonumber \] The symbol "\( \to \)" means "approaches" or, less formally, "gets very close to".
