Find the domain of the function below (in a format of a comma-separated list). y = \boxed{\space}. a_n = \frac {n^3}{5n + 8}, Determine whether the sequence converges or diverges. There may be more than one correct answer. 5 x D 2 x 3 Multiply the indicated polynomials and simplify. Evaluate the limits. r 0, Find a Cartesian ( xy -coordinates) equation of the curve given in polar coordinates: a) r = 2 \sin (\theta) \\ b) r = 3 \cos(\theta) \\ c) r = 2 \\ d) \theta = \frac{\pi}{4}, Find a polar equation for the curve represented by the given Cartesian equation: a).x^2 + y^2 = 4 , \\ b). Find the domain of f. Use polar Coordinates to evaluate \iiint_R \sqrt{x^2 + t^2}\ dA, where R is the region bounded by the circle x^2 + y^2 = 2y. Section 2.4 can help answer this question. {a_n} = {{\ln \left( {n + 2} \right)} \over {\sqrt n }}, State the indeterminate form present (if any) and then evaluate the limit. Use l'Hospital's Rule if appropriate. r = 3 - 2 cos \theta. For f(x) = sqrt(x) and g(x) = x^2 - 1, find: (A) f(g(-2)), (B) g(f(x)). Services, Working Scholars® Bringing Tuition-Free College to the Community. Given two pairs of equations. For the function f(x) = \frac {3x}{(x - 4)^2}: (a) State the domain. Then use transformations of this graph to graph the given function. The region bounded by all leaves of the rose r = 5cos(30). \lim_{n \to \infty} \displaystyle \sum_{i=1}^{n} \dfrac{2}{n} \bigg [ \bigg ( \dfrac{i}{n} \bigg )^3 + 1 \bigg ], Use L'Hospital's Rule to evaluate the limit. in Physics and Engineering, Exercises de Mathematiques Utilisant les Applets, Trigonometry Tutorials and Problems for Self Tests, Elementary Statistics and Probability Tutorials and Problems, Free Practice for SAT, ACT and Compass Math tests, Questions and Answers on Continuity of Functions. y \leq \frac{4}{3}x - 4, Graph the linear inequality. Show that as x , ( 1 + 1 x 2 ) x 1 . (-6,6) (i) Find polar coordinates (r,\theta) of the point, where r is greater than 0 and 0 less than or equal to \theta less than 2\pi. -6|-3 + 3v| less than or equal to 54, For f(x) = -x^3 + 5x^2 - 3x + 2 Determine: a) the domain b) critical value(s) c) intervals where it is increasing and decreasing d) the intervals of concavity e) points of inflection f) end behavior, Find the limit of the following sequence or determine that the limit does not exist. For this reason, the mathematics department set out to create a new course with a speciﬁc set of goals in mind: • A review of the essential mathematicsneeded to succeed in calculus. The circle (x - 5)^2 + (y - 7)^2 = 4 can be drawn with parametric equations. For $12.95 per month, you can stream an unlimited number of movies through an internet service. lim x 0 ( 1 ln x x x 1 ), Solve the following limit using L'Hopital's rule. A set of questions on the concepts of a function, in calculus, are presented along with their answers and solutions. Limit_{(x,y,z) to (-1 pi, 0)} 2017 cos(xy) - z/x + y + z^2. Chapter 2 Overview The concept of limit is one of the ideas that distinguish calculus from … Find the limit. Each bracelet is made... Find the equation of a line passing through the origin so that the sine of the angle between the line in QI and the positive x-axis is \sqrt{2}/2. Chapter 8: Conic Sections Exploration Activity, Explorer Tool: http://illuminations.nctm.org/Activity.aspx?id=3506, Activity Questions: http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/CuttingConics-AS.pdf, http://illuminations.nctm.org/Activity.aspx?id=3506, http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/CuttingConics-AS.pdf. Given the polar points: a) 2 30 o b) 3 60 0 Find the ( x , y ) points.