The value a function approaches as input approaches a point; the foundation of calculus.
The limit of f(x) as x→a is the value f approaches. Limits define derivatives and integrals. Techniques: substitution, factoring, rationalising, squeeze theorem and L'Hôpital's rule for 0/0 or ∞/∞ forms.
lim (x²-1)/(x-1) as x→1 equals 2 after cancelling (x-1).
Limits describe what happens near a point, and they define derivatives and integrals, so every calculus method depends on them.
The value a function approaches as input approaches a point; the foundation of calculus.
Limits describe what happens near a point, and they define derivatives and integrals, so every calculus method depends on them.
It evaluates limits of the form zero over zero or infinity over infinity by taking derivatives of the top and bottom.
Yes. A limit depends on values near the point, not on the value at the point itself.
Typical applications include finding the value of a ratio when both numerator and denominator go to zero, describing the steady-state value of a response as time goes to infinity and checking a safety limit as load approaches a maximum.
Study "Euler's formula" first (topic 24 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
One-sided limits can differ. Limits at infinity describe asymptotes. lim sin x/x =1 as x→0.
lim (x²-1)/(x-1) as x→1 equals 2 after cancelling (x-1).
The next topic is "Continuity", which builds directly on this one.
It is classed as Beginner in Engineering Mathematics (topic 25 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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