Calculus Je |Complete Study Guide With 100% Accurate Questions & Answers | Ace Every Test | Guaranteed Excellence.

CALCULUS JE |COMPLETE STUDY GUIDE WITH 100%
ACCURATE QUESTIONS & ANSWERS | ACE EVERY TEST |
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1.) F(c) exists
2.) limit F(x) as x approaches c exists
3.) limit F(x) as x approaches c = F(c) Answer: f is continuous at x=c if...
Yes lim+=lim-=f(c)
No, f'(c) doesn't exist because of cusp 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'' Answer: Given f'(x):
Is f continuous @ c?
Is there an inflection point on f @ C?
Squeeze Theorem Answer: Define:
Define the Squeeze Theorem. 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 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) Answer: Define the Intermediate Value Theorem.
Global Definition of a Derivative Answer: Define:


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, the limit of {[f(x ⍖ Δx) - f(x)]/Δx} (as Δx approaches 0) Answer: What is the Global
Definition of a Derivative?
Alternative Definition of a Derivative 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) Answer: What is the Alternative
Definition of a Derivative?
The position function OR s(t) Answer: Define:
-16t² ⍖ v₀t ⍖ s₀ Answer: What is the position function OR s(t)
Extreme Value Theorem 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.
Answer: Define the Extreme Value Theorem.
Critical Number 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 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)?
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). Answer: Define Rolle's Theorem.
Mean Value Theorem Answer: What theorem states that the instantaneous rate of change will
equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to
the secant line.
The instantaneous rate of change will equal the mean rate of change somewhere in the interval.
Or, the tangent line will be parallel to the secant line.
f '(c) = [f(b) - f(a)]/[b - a] Answer: Define the Mean Value Theorem.

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