You can fail calculus like any other school subject...you can not study for exams, not do the homework, not understand the course, disturb the class...the possibilities are endless.
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No. Chances are it will be the other way around: if you are bad at math, you stand a good chance of failing calculus or linear algebra. You will perform best at calculus and algebra if you have a strong math background.
Calculus; by a long shot.
Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
It is certainly used in calculus, just as calculus can be used in trigonometry.
No. Calculus if a field of mathematics.