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Review questions for exam ii of math 105, covering topics such as finding derivatives, antiderivatives, and analyzing functions. Questions include finding dy/dx for various functions, determining if points lie on a curve, finding tangent lines, and evaluating roots, critical points, and extrema. Additionally, there are questions on sketching functions and adjusting answers for restricted domains.
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Math 105: Review for Exam II
(a) y = x^2 + 2x^ + e^2 + e^2 x^ + ln 2 + ln (2x) + arctan 2
(b) y =
x · arctan (5x)
(c) y = ln(tan(2cos(x
(^2) ) ))
(d) y =
x + eπ cos 4 + sin^5 (6x)
xy (known as the Folium of Descartes).
(a) Find dy/dx.
(b) Verify that the point (1,2) is on the curve above.
(c) Find the equation of the tangent line at the point (1,2).
(a) an antiderivative of y =
1 − 9 x^2
(b) tan(arccos x) (rewritten as an algebraic expression - no trigonometric functions)
(a) Find the x-value(s) of all roots (x-intercepts) of f.
(b) Find the x- and y-value(s) of all critical points and identify each as a local max, local min, or neither.
(c) Find the x- and y-value(s) of all global extrema and identify each as a global max or global min.
