There are many reasons for a student to fail a course and I have heard most of them. Begging your professor to allow you to pass when your final grade in the course is below the 70% level is not only useless, but cruelly places the sympathy card on your professor. Begging to pass makes it seem like you are unjustly placing the burden of responsibility for your grade on your professor.
"I don't believe the most successful people are the ones who got the best grades, got into the best schools, or made the most money."
- Ben Stein
I get it - trust me, I do. You may have been sick for a portion of the semester. You might learn at a slower pace than most. You may have had a family emergency. You may have given birth! You had to work and go to school at the same time. You were juggling too many courses. You tried really hard, but it wasn't until the very end of the course. All of these excuses (and many more) seem to most in your situation to be viable reasons for a "second chance."
Unfortunately, second chances and "last minute miracles" play no role in determining your true knowledge of the material in a course. If you don't know the material to at least a certain level of proficiency, you cannot pass - period. Generally speaking, students in this "beg for the pass" situation are not here because they did well throughout the course and suddenly bombed the final. They are here because they did poorly throughout the course and on the final.
My Style: You should work hard throughout the semester to make sure you are not in this position. At the end of the semester, I am thinking about the fact that most of my students are going to move into the next course in the math sequence (whether or not this is true for you makes no difference). Those who could not earn a C in my course will likely fail the next course in the sequence if I "show pity" and pass them. Hence, 70% is a C - not 69.9%.