Limits And Continuity

The limit of a function f(x)

The limit of a function f(x) as x approaches 'a' is the value that f(x) gets arbitrarily close to as x gets closer to 'a'. Mathematically: lim(x→a) f(

LHL

LHL: lim(x→a⁻) f(x) is the limit as x approaches 'a' from the left. RHL: lim(x→a⁺) f(x) is the limit as x approaches 'a' from the right. For a limit t

1) Direct Substitution

1) Direct Substitution: Simply substitute the value if no indeterminate form results. 2) Factorization: Factor numerator and denominator to cancel com

Key standard limits include

Key standard limits include: lim(x→0) sin x/x = 1, lim(x→0) (1-cos x)/x² = 1/2, lim(x→0) (e^x - 1)/x = 1, lim(x→0) (1+x)^(1/x) = e, lim(x→0) log(1+x)/

For indeterminate forms 0/0 or ∞/∞

For indeterminate forms 0/0 or ∞/∞, if lim(x→a) f(x)/g(x) gives these forms, then lim(x→a) f(x)/g(x) = lim(x→a) f'(x)/g'(x), provided the right-hand l