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Duplicate of APCALCFINAL
Duplicate of APCALCFINAL
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Answers
1
Find the limit as x approaches infinity of (3x
2
-1) / (x
2
+30x)
Infinity
3
-Infinity
0
2
What equation must be used to find the volume of a sphere?
(pi)r2
4/3(pi)r3
2(pi)r
4/3(pi)r2
3
Find the derivative of 2
x
(2x)ln(2)
x2x
x22x
2(ln2)(2x)
4
Factor (X
3
-216)
(x-6)(x2-6x+36)
(x-6)(x2+6x-36)
(x-6)(x2+6x+36)
(x+6)(x2+6x+36)
5
For a function, the instantaneous rate of change is the same as...?
Average Rate of Change
Slope of the Tangent Line
Limit as X-->2
Slope of the Secant Line
6
Which is NOT a critical point?
Where F(x) is undefined
F''(0)
F'(0)
The endpoints
7
What is the power rule for derivatives?
F'(x)=nx(n-1)
F'(x)=x(n-1)
F'(x)=ex
H'(x)=g'(x)+f'(x)
8
There is a relative minimum at F(c) when...?
F''(c)>0
F'(c)=0 and F''(c)<0
F(c)=0 and F'(c)>0
F'(c)=0 and F''(c)>0
9
When is F(x) concave up?
F''(x)<0
F'(x)<0
F''(x)>0
F'(x)>0
10
What is the vertical asymptote of F(x)=(x
2
+1)/(x
2
-1)?
X=0,-1
None of the above
X=0,1
X=1,-1
11
F is a continuous function at C when...?
F(c) is defined
Limx-->c F(x) exists
Limx-->c F(x)=F(c)
All of the above are required
12
If a function is differentiable, then...
It is not continuous
It does not exist
It's continuous
None of the above
13
Conversely: If F is differentiable as X=C, then F must be continuous at X=C
True
False
14
The derivative is _______, whereas the integral is the _____.
A rate, Area under the curve
A rate, Anti-derivative
Slope, Anti-derivative
All of the above
15
L'Hopital's Rule states that: Lim f(x)/g(x)=
(LoDHi-HiDLo)/(Lo2)
Lim F(x)/G'(x)
Lim F(x)/g'(x)
You're toast if you get 0/0
16
What is the derivative of sin
-1
(5x)
5/√(1-25x2)
5/√(1+25x2)
cos(5x)
5sin-2(5x)
17
Who showed up to class more: Noushi or Jack?
Jack
All of the above
They didn't
Noushi
18
What is the absolute maximum point of the function f(x)=18cos(x/2) on (0,2)?
(0,5)
None of the above
(2,7)
(0,18)
19
What is the antiderivative of F'(x)=x
-7
F(x)=1/6x6
F(x)=-1/6x6+C
F(x)=-1/7x7+C
F(x)=1/6x6+C
20
If F is continuous as X=C, then F is differentiable at X=C
False
True
21
Which is NOT a part of the definition of a continuous function?
F(a) exists
Limit as x approaches a of F(x)=F(a)
The function is differentiable
Limit as x approaches a of F(x) exists
22
What is the rule to deriving fractions?
(LoDhi-HiDlo) / (Lo2)
(HiDLo-LoDHi) / (Hi2)
(DHi-DLo) / (HiLo2)
LoDHi-HiDLo
23
From taking Calculus this year, you can find true love...
True, you fell deeply in love with calculus
False, your heart breaks just thinking about calculus
24
Which existence theorem proves that there is a value C=0 in between points X= -4 and X=6?
Mean Value Theorem
Pythagorean Theorem
Intermediate Value Theorem
Constant Rule
25
What is shown below?
First derivative test
Definition of a derivative
Alternative form of the derivative
Mean Value Theorem
