Calculus

Calculus A+ GRADE A Q*A


1.) F(c) exists
2.) limit F(x) as x approaches c exists
3.) limit F(x) as x approaches c = F(c) - (CORRECT ANSWER)f is continuous at x=c
if...

Yes lim+=lim-=f(c)
No, f'(c) doesn't exist because of cusp - (CORRECT ANSWER)Given f(x):
Is f continuous @ C
Is f' continuous @ C

This is a graph of f'(x). Since f'(C) exists, differentiability implies continuouity, so Yes.
Yes f' decreases on X<C so f''<0
f' increases on X>C so f''>0
A point of inflection happens on a sign change at f'' - (CORRECT ANSWER)Given
f'(x):
Is f continuous @ c?
Is there an inflection point on f @ C?

1 - (CORRECT ANSWER)

0 - (CORRECT ANSWER)

Squeeze Theorem - (CORRECT ANSWER)Define:

Define the Squeeze Theorem. - (CORRECT ANSWER)Suppose that g(x)≤f(x) and
also suppose that {the limit of g(x) (as x goes to a)} = {the limit of h(x) (as x goes to
a)} = L
then
{the limit of f(x) (as x goes to a) = L}

Intermediate Value Theorem - (CORRECT ANSWER)What is the name of the
theorem that states: "if f is continuous on [a,b] and k is a number between f(a) and
f(b), then there exists at least one number c such that f(c)?"

If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists
at least one number c such that f(c) - (CORRECT ANSWER)Define the Intermediate
Value Theorem.

Global Definition of a Derivative - (CORRECT ANSWER)Define:

the limit of {[f(x ⍖ Δx) - f(x)]/Δx} (as Δx approaches 0) - (CORRECT ANSWER)What
is the Global Definition of a Derivative?

Alternative Definition of a Derivative - (CORRECT ANSWER)Define: f '(x) is the limit
of the following difference quotient as x approaches c

, f '(x) is the limit of "[f(x)-f(c)]/[x-c]" (as x approaches c) - (CORRECT ANSWER)What
is the Alternative Definition of a Derivative?

nx^(n-1) - (CORRECT ANSWER)

1 - (CORRECT ANSWER)

cf'(x) - (CORRECT ANSWER)

f'(x)+g'(x) - (CORRECT ANSWER)

The position function OR s(t) - (CORRECT ANSWER)Define:

-16t² ⍖ v₀t ⍖ s₀ - (CORRECT ANSWER)What is the position function OR s(t)

f'(x)-g'(x) - (CORRECT ANSWER)

uvw'+uv'w+u'vw - (CORRECT ANSWER)

cos(x) - (CORRECT ANSWER)

-sin(x) - (CORRECT ANSWER)

sec²(x) - (CORRECT ANSWER)

-csc²(x) - (CORRECT ANSWER)

sec(x)tan(x) - (CORRECT ANSWER)

dy/dx - (CORRECT ANSWER)

The Chain Rule: f'(g(x))g'(x) - (CORRECT ANSWER)

Extreme Value Theorem - (CORRECT ANSWER)What theorem states that if f is
continuous on [a,b] then f has an absolute maximum and an absolute minimum on
[a,b]. The global extrema occur at critical points in the interval or at endpoints of the
interval?

If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum
on [a,b]. The global extrema occur at critical points in the interval or at endpoints of
the interval. - (CORRECT ANSWER)Define the Extreme Value Theorem.

Critical Number - (CORRECT ANSWER)If f'(c)=0 or does not exist, and c is in the
domain of f, then c is a what? (Derivative is 0 or undefined)

Rolle's Theorem - (CORRECT ANSWER)What theorem states that if we let f be
continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least
one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative
must = 0 somewhere in the interval)?