1 Limits And Continuity 2 The Derivative 3 Topics In Differentiation 4 The Derivative In Graphing And Applications 5 Integration 6 Applications Of The Definite Integral In Geometry, Science, And Engineering 7 Principles Of Integral Evaluation 8 Mathematical Modeling With Differential Equations 9 Infinite Series 10 Parametric And Polar Curves; Conic Sections 11 Three-dimensional Space; Vectors 12 Vector-valued Functions 13 Partial Derivatives 14 Multiple Integrals 15 Topics In Vector Calculus expand_more
12.1 Introduction To Vector-valued Functions 12.2 Calculus Of Vector-valued Functions 12.3 Change Of Parameter; Arc Length 12.4 Unit Tangent, Normal, And Binormal Vectors 12.5 Curvature 12.6 Motion Along A Curve 12.7 Kepler’s Laws Of Planetary Motion Chapter Questions expand_more
Problem 1QCE: alimt3t2i+2tj=blimt/4cost,sint= Problem 2QCE: Find r t. art=4+5ti+tt2jbrt=1t,tant,e2t Problem 3QCE: Suppose that r10=3,2,1,r20=1,2,3,r 10=0,0,0,andr 20=6,4,2. Use this information to evaluate the... Problem 4QCE: a012t,t2,sintdt=bti3t2j+etkdt= Problem 1ES: Find the limit. limt+t2+13t2+2,1t Problem 2ES Problem 3ES: Find the limit. limt2ti3j+t2k Problem 4ES Problem 5ES: Determine whether rt is continuous at t=0. Explain your reasoning. art=3sinti2tjbrt=t2i+1tj+tk Problem 6ES: Determine whether rt is continuous at t=0. Explain your reasoning. art=eti+j+csctkbrt=5i3t+1j+e2tk Problem 7ES: Sketch the circle rt=costi+sintj, draw the vector with its correct length. ar /4br cr2r3/2 Problem 8ES Problem 9ES: Find r t. rt=4icostj Problem 10ES: Find r t. rt=tan1ti+tcostjtk Problem 11ES Problem 12ES Problem 13ES Problem 14ES: Find the vector rt0; then sketch the graph of rt in 2-space and draw the tangent vector rt0.... Problem 15ES: Find the vector rt0; then sketch the graph of rt in 3-space and draw the tangent vector rt0.... Problem 16ES Problem 17ES Problem 18ES Problem 19ES: Find parametric equations of the line tangent to the graph of rt at the point where t=t0.... Problem 20ES Problem 21ES: Find parametric equations of the line tangent to the graph of rt at the point where t=t0.... Problem 22ES Problem 23ES Problem 24ES: Find a vector equation of the line tangent to the graph of rt at the point P0 on the curve.... Problem 25ES Problem 26ES Problem 27ES: Letrt=costi+sintj+k.findalimt0rtr tblimt0rtr tclimt0rtr t. Problem 28ES Problem 29ES: Calculate ddtr1tr2tandddtr1tr2t first by differentiating the product directly and then by applying... Problem 30ES: Calculate ddtr1tr2tandddtr1tr2t first by differentiating the product directly and then by applying... Problem 31ES: Evaluate the indefinite integral. 3i+4tjdt Problem 32ES Problem 33ES: Evaluate the indefinite integral. tet,lntdt Problem 34ES: Evaluate the indefinite integral. et,et,3t2dt Problem 35ES: Evaluate the definite integral. 0/2cos2t,sin2tdt Problem 36ES Problem 37ES: Evaluate the definite integral. 02ti+t2jdt Problem 38ES Problem 39ES: Evaluate the definite integral. 19t1/2i+t1/2jdt Problem 40ES: Evaluate the definite integral. 01e2ti+etj+tkdt Problem 41ES Problem 42ES Problem 43ES Problem 44ES Problem 45ES: Solve the vector initial-value problem for yt by integrating and using the initial conditions to... Problem 46ES: Solve the vector initial-value problem for yt by integrating and using the initial conditions to... Problem 47ES Problem 48ES: Solve the vector initial-value problem for yt by integrating and using the initial conditions to... Problem 49ES: (a) Find the points where the curve r=ti+t2j3tk intersects the plane 2xy+z=2. (b) For the curve and... Problem 50ES Problem 51ES: Show that the graphs of r1tandr2t intersect at the point P. Find, to the nearest degree, the acute... Problem 52ES: Show that the graphs of r1tandr2t intersect at the point P. Find, to the nearest degree, the acute... Problem 53ES: Use Formula (7) to derive the differentiation formula ddtrtr trtr t Problem 54ES: Let u=ut,v=vt,andw=wt be differentiable vector-values functions. Use formulas (6) and (7) to show... Problem 55ES: Let u1,u2,u3,1,2,3,w1,w2,andw3, be differentiable functions of t. Use Exercise 54 to show that... Problem 56ES: Prove Theorem 12.2.6 for 2-space. Problem 57ES: Derive Formulas (6) and (7) for 3-space. Problem 58ES: Prove Theorem 12.2.9 for 2-space. Problem 59ES Problem 60ES format_list_bulleted
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning