Limits: When A Function Fails To Reach A Definite Value At A Point
When does a limit not exist (one sided limit) If two limits on the same graph arelim (x→ 0^+) f(x) = 1lim (x→ 0^-) f(x) = 0...
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John Rhodes
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June 21, 2023
Mathematical Existence: Prohibitions On Division By Zero And Imaginary Numbers
Two ways a function can’t exist If a limit of a function is an unstable number and it keeps changing, such as sin (π/x) which forever oscillates...
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John Rhodes
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June 21, 2023
Mastering Infinite Limits: Techniques For Evaluating Functions Approaching Infinity
Infinite limits lim ( x→ a) f(x) = ∞. is an infinite limit. This means that as x approaches zero, f(x) gets larger and larger. Examplelim (...
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John Rhodes
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June 21, 2023
Vertical Asymptotes In Math: Definition, Equation, And Importance
Vertical asymptote whenever you have a limit in which x approaches a from the left or right or left and right and f(x) approaches positive or negative...
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John Rhodes
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June 21, 2023
Mastering Limit Laws: Rules To Evaluate Limits Of Well-Behaved Math Functions
Limit laws Sum lawlim ( x→ a) [ f(x) + g(x) ] = lim ( x→ a) f(x) + lim ( x→ a) g(x)Difference lawlim ( x→...
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John Rhodes
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June 21, 2023
The Greatest Integer Function: Definition, Properties, And Applications
Greatest integer function Basically ⌊x⌋ = the greatest INTEGER smaller or equal to xFor example:⌊4.8⌋ = 4 ⌊6.5⌋ = 6. ⌊π⌋= 3Also, the greatest integer function is...
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John Rhodes
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June 21, 2023
How To Find Limits With The Squeeze Theorem In Math
Squeeze theory (AKA sandwich theory or pinch theory) for limit functions f(x) ≤ g(x). when x is near a (but possibly not a) thenlim (x → a)...
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John Rhodes
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June 21, 2023
The Precise Definition Of Limits In Mathematics: The Behavior Of Functions As Inputs Approach A Point
Precise definition of a limit (ALSO, precise definition is also known as delta – epsilon limit or ε – &). if lim (x → a) f(x) =...