Trapezoidal approx of \(\displaystyle\int_{0}^{10} f(x) d x\) where \(f\) values: \(f(0)=20, f(1)=19.5, f(2)=18, f(3)=15.5, f(4)=12, f(5)=7.5, f(6)=2, f(7)=-4.5, f(8)=-12, f(9)=-20.5, f(10)=-30\)
A
\(30.825\)
✕
B
\(32.500\)
✕
C
\(33.325\)
✕
D
\(33.333\)
✕
E
\(35.825\)
✕
Question 23 of 35
| MCQ
· Level 2
For which pair \(f, g\) is \(\lim \dfrac{f}{g} = 0\)?
A
\(e^x, x^2\)
✕
B
\(e^x, \ln x\)
✕
C
\(\ln x, e^x\)
✕
D
\(x, \ln x\)
✕
E
\(3^x, 2^x\)
✕
Question 24 of 35
| MCQ
· Level 3
Table near \(x=0\): \(f(x)\) approaches 2, \(g\) jumps from 1 (left) to 2 (right), \(h\) approaches 2 from both sides. For which functions does limit at 0 equal 2?
A
\(f\) only
✕
B
\(g\) only
✕
C
\(h\) only
✕
D
\(f\) and \(h\) only
✕
E
\(f, g\), and \(h\)
✕
Question 25 of 35
| MCQ
· Level 4
\(f(x) = |(x^2 - 12)(x^2 + 4)|\) on \(-2 < x < 3\). How many \(c\) satisfy MVT conclusion?
A
None
✕
B
One
✕
C
Two
✕
D
Three
✕
E
Four
✕
Question 26 of 35
| MCQ
· Level 3
\(A(t) = 4000 + 48(t - 3) - 4(t - 3)^3\). Production rate is increasing most rapidly at
A
8:00 am
✕
B
10:00 am
✕
C
11:00 am
✕
D
12:00 am
✕
E
1:00 pm
✕
Question 27 of 35
| MCQ
· Level 4
\(y = 4 x^5 - 3 x^4 + 15 x^2 + 6\). How many points \(a\) on the curve have tangent through origin?
A
One
✕
B
Two
✕
C
Three
✕
D
Four
✕
E
Five
✕
Question 28 of 35
| MCQ
· Level 4
[Calc] \(P(t) = 6000 - 5500 e^{-0.159 t}\) for \(t \geq 0\). During which year does \(P\) reach half its limiting value?
A
Second
✕
B
Third
✕
C
Fourth
✕
D
Eighth
✕
E
Twenty-ninth
✕
Question 29 of 35
| MCQ
· Level 3
Which value is NOT in domain of \(f(x) = (\cos x)^x\)?
A
\(1\)
✕
B
\(\dfrac{\pi}{2}\)
✕
C
\(4 \dfrac{\pi}{3}\)
✕
D
\(4\)
✕
E
\(2 \pi\)
✕
Question 30 of 35
| MCQ
· Level 2
\(f\) everywhere differentiable. \(f'\) values: \(f'(-10)=-2\), \(f'(-5)=-1\), \(f'(0)=0\), \(f'(5)=1\), \(f'(10)=2\). \(f'\) always increasing. Which must be true?
A
\(f\) has rel min at \(x = 0\)
✕
B
\(f\) concave down for all \(x\)
✕
C
\(f\) has inflection at \((0, f(0))\)
✕
D
\(f\) passes through origin
✕
E
\(f\) is odd
✕
Question 31 of 35
| MCQ
· Level 4
[Calc] \(f'(x) = e^x(-x^3 + 3 x) - 3\) for \(0 \leq x \leq 5\). At what value of \(x\) is \(f\) absolute minimum?
[Calc] Midpoint Riemann sum for \(\displaystyle\int_{0}^{6} f(x) d x\) with 3 intervals of width 2, table \(f(0)=0, f(1)=0.25, f(2)=0.48, f(3)=0.68, f(4)=0.84, f(5)=0.95, f(6)=1\)
A
\(2.64\)
✕
B
\(3.64\)
✕
C
\(3.72\)
✕
D
\(3.76\)
✕
E
\(4.64\)
✕
Question 35 of 35
| MCQ
· Level 3
Tangent to \(y = e^{2-x}\) at \((1, e)\) intersects axes. Triangle area?
A
\(2 e\)
✕
B
\(e^2 - 1\)
✕
C
\(e^2\)
✕
D
\(2 e \sqrt{e}\)
✕
E
\(4 e\)
✕
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Graphing Calculator
Reference Sheet
Area & Circumference
Circle$A = \pi r^2$, $C = 2\pi r$
Rectangle$A = lw$
Triangle$A = \tfrac{1}{2}bh$
Trapezoid$A = \tfrac{1}{2}(b_1+b_2)h$
Volume
Box$V = lwh$
Cylinder$V = \pi r^2 h$
Sphere$V = \tfrac{4}{3}\pi r^3$
Cone$V = \tfrac{1}{3}\pi r^2 h$
Pyramid$V = \tfrac{1}{3}lwh$
Triangles
Pythagorean Thm$a^2 + b^2 = c^2$
30-60-90sides: $1,\, \sqrt{3},\, 2$
45-45-90sides: $1,\, 1,\, \sqrt{2}$
Triangle Anglessum $= 180°$
Other Facts
Circle Degrees$360° = 2\pi \text{ rad}$
Exterior Angle= sum of non-adjacent interior angles
The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is $2\pi$.
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