You typically don’t need to provide writing examples in your resume and cover letter, but be prepared to send them separately to employers if requested. In a way, your cover letter and resume will be examples of your writing skills. You need to use great resume action words, proofread your resume with spell check a few times and spend some time revising the resume before you apply.
If the job application does request a writing sample, include your absolute best writing pieces that fit well within the confines of the job. For example, include business writing samples if that’s going to be what you write if you get hired. You may also want to bring a few friends onboard as proofreaders who can look over your writing sample and make sure it reads well.