MAC 2311 - Exam 1 questions with
correct answers
Formal Definition of a Limit - correct answer ✔✔ the lim f(x) = L if any ε > 0, there exists a
corresponding δ > 0 such that |f(x)-L| < ε whenever 0 < |x - c| < δ.
simple version: as x approaches to a, function f(x) gets closer to L
Squeeze Theorem - correct answer ✔✔ If f(x) ≤ g(x) ≤ h(x) when x is near a (EXCEPT possibly at
a) and limx→a f(x) = limx→a h(x) = L, then limx→a g(x) = L.
simple version: if a function is always between two other functions that approach the same limit
at a point, then the original function also approaches the limit at that point.
Definition of Continuity - correct answer ✔✔ f(x) is continuous at c if the lim x->c f(x) = f(c)
- NO breaks in the graph
Intermediate Value Theorem - correct answer ✔✔ if f is a continuous function on the interval
from a to b and f(a) ≠ f(b), then for any value N between f(a) and f(b), there exists a z in the
interval such that f(z) = N.
simple version: if a continuous function takes on two values, it must take on every value in
between
Definition of the Derivative of a Function at a Point - correct answer ✔✔ we defined the slope
of the tangent line to
correct answers
Formal Definition of a Limit - correct answer ✔✔ the lim f(x) = L if any ε > 0, there exists a
corresponding δ > 0 such that |f(x)-L| < ε whenever 0 < |x - c| < δ.
simple version: as x approaches to a, function f(x) gets closer to L
Squeeze Theorem - correct answer ✔✔ If f(x) ≤ g(x) ≤ h(x) when x is near a (EXCEPT possibly at
a) and limx→a f(x) = limx→a h(x) = L, then limx→a g(x) = L.
simple version: if a function is always between two other functions that approach the same limit
at a point, then the original function also approaches the limit at that point.
Definition of Continuity - correct answer ✔✔ f(x) is continuous at c if the lim x->c f(x) = f(c)
- NO breaks in the graph
Intermediate Value Theorem - correct answer ✔✔ if f is a continuous function on the interval
from a to b and f(a) ≠ f(b), then for any value N between f(a) and f(b), there exists a z in the
interval such that f(z) = N.
simple version: if a continuous function takes on two values, it must take on every value in
between
Definition of the Derivative of a Function at a Point - correct answer ✔✔ we defined the slope
of the tangent line to
