SURVEY OF CALCULUS EXAM
QUESTIONS AND ANSWERS
definition of finite limits at infinity (limit as x approaches negative infinity) - ANSWER-if
the values of f(x) can be made as close to L as we want by taking x sufficiently "large
negative".
definition of a horizontal asymptote - ANSWER-the horizontal line y=L is a horizontal
asymptote for the graph of the function f if either or both of the following hold: limit of f(x)
as x approaches negative or positive infinity equals L.
definition of continuity - ANSWER-a function f is continuous at x=c if:
limit of f(x) as x approaches c exists
f(c) is defined
limit of f(x) as x approaches c equals f(c).
definition of a partition number - ANSWER-a real number x is a partition number for a
function f if f is discontinuous at x or f(x)=0.
definition of a finite limit at a real number - ANSWER-and we say that "the limit of f(x) as
x approaches c* is L" if we can make the values of f(x) as close to L as we want by
taking x close enough to c on either side of c but not equal to c.
definition of finite one-sided limits at a real number (left) - ANSWER-and we say that
"the limit of f(x) as x approaches c from the left is L" if we can make the values of f(x) as
close to L as we want by taking x close enough to c but less than c.
definition of finite one-sided limits at a real number (right) - ANSWER-and we say that
"the limit of f(x) as x approaches c from the right is L" if we can make the values of f(x)
as close to L as we want by taking x close enough to c but greater than c.
Theorem 1 - ANSWER-let f be a function and c and L are real numbers. we have that
the limit of f(x) as x approaches c is L iff the limit of f(x) as x approaches c from the left
is equal to the limit of f(x) as x approaches c from the right is L.
Theorem 3 (section 2.1) - ANSWER-if the function f is a polynomial or a rational function
and c is in the domain of f then the limit of f(x) as x approaches c is f(c).
definition of an indeterminate form - ANSWER-let c be a real number. if the limit of f(x)
as x approaches c is 0 and the limit of g(x) as x approaches c is 0, then the limit of
f(x)/g(x) as x approaches c is called a 0/0 indeterminate form.
QUESTIONS AND ANSWERS
definition of finite limits at infinity (limit as x approaches negative infinity) - ANSWER-if
the values of f(x) can be made as close to L as we want by taking x sufficiently "large
negative".
definition of a horizontal asymptote - ANSWER-the horizontal line y=L is a horizontal
asymptote for the graph of the function f if either or both of the following hold: limit of f(x)
as x approaches negative or positive infinity equals L.
definition of continuity - ANSWER-a function f is continuous at x=c if:
limit of f(x) as x approaches c exists
f(c) is defined
limit of f(x) as x approaches c equals f(c).
definition of a partition number - ANSWER-a real number x is a partition number for a
function f if f is discontinuous at x or f(x)=0.
definition of a finite limit at a real number - ANSWER-and we say that "the limit of f(x) as
x approaches c* is L" if we can make the values of f(x) as close to L as we want by
taking x close enough to c on either side of c but not equal to c.
definition of finite one-sided limits at a real number (left) - ANSWER-and we say that
"the limit of f(x) as x approaches c from the left is L" if we can make the values of f(x) as
close to L as we want by taking x close enough to c but less than c.
definition of finite one-sided limits at a real number (right) - ANSWER-and we say that
"the limit of f(x) as x approaches c from the right is L" if we can make the values of f(x)
as close to L as we want by taking x close enough to c but greater than c.
Theorem 1 - ANSWER-let f be a function and c and L are real numbers. we have that
the limit of f(x) as x approaches c is L iff the limit of f(x) as x approaches c from the left
is equal to the limit of f(x) as x approaches c from the right is L.
Theorem 3 (section 2.1) - ANSWER-if the function f is a polynomial or a rational function
and c is in the domain of f then the limit of f(x) as x approaches c is f(c).
definition of an indeterminate form - ANSWER-let c be a real number. if the limit of f(x)
as x approaches c is 0 and the limit of g(x) as x approaches c is 0, then the limit of
f(x)/g(x) as x approaches c is called a 0/0 indeterminate form.
