Solutions for CALCULUS,MULTIVARIABLE-W/ACCESS>CUSTOM<
Problem 1E:
Find dy/dx. 1. x=t1+t,y=1+tProblem 2E:
Find dy/dx. 2. x = tet, y = t + sin tProblem 3E:
Find an equation of the tangent to the curve at the point corresponding to the given value of the...Problem 4E:
Find an equation of the tangent to the curve at the point corresponding to the given value of the...Problem 5E:
Find an equation of the tangent to the curve at the point corresponding to the given value of the...Problem 6E:
Find an equation of the tangent to the curve at the point corresponding to the given value of the...Problem 7E:
Find an equation of the tangent to the curve at the given point by two methods: (a) without...Problem 12E:
Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 12. x = t3 + 1, y = t2 tProblem 13E:
Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 13. x = et, y = tetProblem 15E:
Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 15. x = t ln t, y = t +...Problem 16E:
Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 16. x = cos t, y = sin...Problem 17E:
Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing...Problem 19E:
Find the points on the curve where the tangent is horizontal or vertical. If you have a graphing...Problem 22E:
Use a graph to estimate the coordinates of the lowest point and the leftmost point on the curve x =...Problem 24E:
Graph the curve in a viewing rectangle that displays all the important aspects of the curve. 24. x =...Problem 26E:
Graph the curve x = 2 cos t, y = sin t + sin 2t to discover where it crosses itself. Then find...Problem 27E:
(a) Find the slope of the tangent line to the trochoid x = r d sin , y = r d cos in terms of ....Problem 28E:
(a) Find the slope of the tangent to the astroid x = a cos3, y = a sin3 in terms of . (Astroids are...Problem 29E:
At what point(s) on the curve x = 3t2 + 1, y = t3 1 does the tangent line have slope 12?Problem 30E:
Find equations of the tangents to the curve x = 3t2 + 1, y = 2t3 + 1 that pass through the point (4,...Problem 31E:
Use the parametric equations of an ellipse, x = a cos , y = b sin , 0 2, to find the area that it...Problem 34E:
Find the area of the region enclosed by the astroid x = a cos3, y = a sin3. (Astroids are explored...Problem 36E:
Let R be the region enclosed by the loop of the curve in Example 1. (a) Find the area of R. (b) If R...Problem 38E:
Set up an integral that represents the length of the curve. Then use your calculator to find the...Problem 49E:
Use Simpsons Rule with n = 6 to estimate the length of the curve x = t et, y = t + et, 6 t 6.Problem 50E:
In Exercise 10.1.43 you were asked to derive the parametric equations x = 2a cot , y = 2a sin2 for...Problem 51E:
Find the distance traveled by a particle with position (x, y) as t varies in the given time...Problem 52E:
Find the distance traveled by a particle with position (x, y) as t varies in the given time...Problem 55E:
(a) Graph the epitrochoid with equations x=11cost4cos(11t/2)y=11sint4sin(11t/2) What parameter...Problem 63E:
Find the exact area of the surface obtained by rotating the given curve about the x-axis. 63. x = a...Problem 65E:
Find the surface area generated by rotating the given curve about the y-axis. 65. x = 3t2, y = 2t3,...Problem 66E:
Find the surface area generated by rotating the given curve about the y-axis. 66. x = et t, y =...Problem 67E:
If f is continuous and f(t) 0 for a t b, show that the parametric curve x = f(t), y = g(t), a t ...Problem 69E:
The curvature at a point P of a curve is defined as =|dds| where is the angle of inclination of the...Problem 70E:
(a) Use the formula in Exercise 69(b) to find the curvature of the parabola y = x2 at the point (1,...Problem 71E:
Use the formula in Exercise 69(a) to find the curvature of the cycloid x = sin , y = 1 cos at...Problem 72E:
(a) Show that the curvature at each point of a straight line is = 0. (b) Show that the curvature at...Browse All Chapters of This Textbook
Chapter 10 - Parametric Equations And Polar CoordinatesChapter 10.1 - Curves Defined By Parametric EquationsChapter 10.2 - Calculus With Parametric CurvesChapter 10.3 - Polar CoordinatesChapter 10.4 - Areas And Lengths In Polar CoordinatesChapter 10.5 - Conic SectionsChapter 10.6 - Conic Sections In Polar CoordinatesChapter 11 - Infinite Sequences And SeriesChapter 11.1 - SequencesChapter 11.2 - Series
Chapter 11.3 - The Integral Test And Estimates Of SumsChapter 11.4 - The Comparison TestsChapter 11.5 - Alternating SeriesChapter 11.6 - Absolute Convergence And The Ratio And Root TestsChapter 11.7 - Strategy For Testing SeriesChapter 11.8 - Power SeriesChapter 11.9 - Representations Of Functions As Power SeriesChapter 11.10 - Taylor And Maclaurin SeriesChapter 11.11 - Applications Of Taylor PolynomialsChapter 12 - Vectors And The Geometry Of SpaceChapter 12.1 - Three-dimensional Coordinate SystemsChapter 12.2 - VectorsChapter 12.3 - The Dot ProductChapter 12.4 - The Cross ProductChapter 12.5 - Equations Of Lines And PlanesChapter 12.6 - Cylinders And Quadric SurfacesChapter 13 - Vector FunctionsChapter 13.1 - Vector Functions And Space CurvesChapter 13.2 - Derivatives And Integrals Of Vector FunctionsChapter 13.3 - Arc Length And CurvatureChapter 13.4 - Motion In Space: Velocity And AccelerationChapter 14 - Partial DerivativesChapter 14.1 - Functions Of Several VariablesChapter 14.2 - Limits And ContinuityChapter 14.3 - Partial DerivativesChapter 14.4 - Tangent Planes And Linear ApproximationsChapter 14.5 - The Chain RuleChapter 14.6 - Directional Derivatives And The Gradient VectorChapter 14.7 - Maximum And Minimum ValuesChapter 14.8 - Lagrange MultipliersChapter 15 - Multiple IntegralsChapter 15.1 - Double Integrals Over RectanglesChapter 15.2 - Double Integrals Over General RegionsChapter 15.3 - Double Integrals In Polar CoordinatesChapter 15.4 - Applications Of Double IntegralsChapter 15.5 - Surface AreaChapter 15.6 - Triple IntegralsChapter 15.7 - Triple Integrals In Cylindrical CoordinatesChapter 15.8 - Triple Integrals In Spherical CoordinatesChapter 15.9 - Change Of Variables In Multiple IntegralsChapter 16 - Vector CalculusChapter 16.1 - Vector FieldsChapter 16.2 - Line IntegralsChapter 16.3 - The Fundamental Theorem For Line IntegralsChapter 16.4 - Green's TheoremChapter 16.5 - Curl And DivergenceChapter 16.6 - Parametric Surfaces And Their AreasChapter 16.7 - Surface IntegralsChapter 16.8 - Stokes' TheoremChapter 16.9 - The Divergence TheoremChapter 17 - Second-order Differential EquationsChapter 17.1 - Second-order Linear EquationsChapter 17.2 - Nonhomogeneous Linear EquationsChapter 17.3 - Applications Of Second-order Differential EquationsChapter 17.4 - Series SolutionsChapter G - Complex Numbers
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