IPA: /ˌʌn.hɪˈzeɪ.tɪŋ.li/
KK: /ʌnˈhɛzɪteɪɪŋli/
In a way that shows no hesitation or doubt; confidently and decisively.
She unhesitatingly accepted the job offer, knowing it was the right choice for her.
Unhesitatingly → It is formed from "un-" (meaning not) and "hesitate" (from Latin "haesitare", meaning to stick or to hesitate) and the suffix "-ly" (meaning in a manner). The word means to do something in a manner that is not hesitant or with certainty.
Think of 'not' ('un-') being combined with 'hesitating' ('haesitare') to remember that 'unhesitatingly' means doing something without any hesitation.