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These are the Exam of Calculus which includes Worst, Wedding Cake, Volume of Cylinder, Very Cold Freezer etc. Key important points are: Taylor Polynomial, Arctan, Curve Defined, Folium of Descartes, Tangent Line, Point, Equation, Limits, Antiderivative, Taylor Polynomial
Typology: Exams
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Math 105: Review for Exam II
(a) y = x
2
x
2
2 x
(b) y =
x · arctan (5x)
(c) y = ln(tan(
cos(x^2 ) ))
(d) y = sin 3
x + e π
ln 4 + arcsin 6x
(e) y = (x 2
sin x
xy (known as the Folium of Descartes).
(a) Find dy/dx.
(b) Find the equation of the tangent line at the point (1,2).
(a) lim x→ 0
sin 3x
5 x
(b) lim x→∞
ex
ln x
(c) lim x→ 0
1 − cos 2x
3 x
(d) lim x→ 1
x 3 − 1
5 − 5 x
(e) lim x→ 0
1 − cos 4x
5 x^2
(a) an antiderivative of y =
1 − 9 x^2
(b) tan(arccos x)
(c) the second degree Taylor polynomial for f(x) =
x based at x = 9
(a) If f ′ (1) = 0 then f always/sometimes/never has a critical point at x = 1.
(b) If f ′ (2) = 0 then f always/sometimes/never has a local maximum or local minimum at x = 2.
(c) If x = 3 is a critical point of f, then f ′ (3) is always/sometimes/never 0.
(d) If f ′′ (4) = 0, then f always/sometimes/never has an inflection point at x = 4.
(e) If f has a global maximum at x = 5, then f ′ (5) is always/sometimes/never 0.
(f) If f ′ (6) = 0 and f ′′ (6) = −2, then f always/sometimes/never has a local maximum at x = 6.
(g) If f
′ (7) = 0 and f
′′ (7) = 0, then f always/sometimes/never has a local extremum at x = 7.
π
arcsin t+y 2 and that f
. Find the equation of the tangent line to f at
Sno-Cone holder, if you prefer) by cutting out a wedge then gluing the new edges together to form a cone. What is the maximum possible volume of the cone? Hint: Pythagorean Theorem.
Note: the volume of a cone is
π
3
r
2 h.
