1 Answer | Add Yours
The limit `lim_(x->1/3)sin(3x-1)/(3x^2+2x-1)` has to be determined.
Substituting x = `1/3` , gives the form `0/0` which is indeterminate. This allows the use of l'Hopital's Rule and the numerator and denominator can be replaced with their derivatives.
= `lim_(x->1/3) ((sin(3x-1))')/((3x^2+2x-1)')`
= `lim_(x->1/3) (3*cos(3x-1))/(6x + 2)`
Substituting x = `1/3` gives `(3*1)/4 = 3/4`
The required limit is 3/4
We’ve answered 319,412 questions. We can answer yours, too.Ask a question