Axioms Posted October 17, 2011 Share Posted October 17, 2011 Hi I need help to determine if the text books answer is wrong. 6th Edition of Calculus Early Transcendentals by James Stewart if you have the book. Its on page 636 question 3. It states: Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x= t^2 + t , y= t^2 - t ; t = 0 It is basic but the answer they give does not make any sense to me. They found the equation of the tangent to be (2sint*cost)/(lnt+1) I found the equation of the tangent to be y=-x I've drawn the curve and it seems to match my answer at t = 0 If somebody could please confirm my answer or tell me if I'm making some kind of error in my calculation it would be appreciated. Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted October 17, 2011 Share Posted October 17, 2011 The book's tangent equation is not defined at t=0, since the natural logarithm is only defined for positive numbers (in the reals, at least). Your tangent equation seems to be correct at t=0, although you should try making a general expression for any t just to get the hang of it. 1 Link to comment Share on other sites More sharing options...
Axioms Posted October 17, 2011 Author Share Posted October 17, 2011 Thanks Link to comment Share on other sites More sharing options...
DrRocket Posted October 17, 2011 Share Posted October 17, 2011 Hi I need help to determine if the text books answer is wrong. 6th Edition of Calculus Early Transcendentals by James Stewart if you have the book. Its on page 636 question 3. It states: Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x= t^2 + t , y= t^2 - t ; t = 0 It is basic but the answer they give does not make any sense to me. They found the equation of the tangent to be (2sint*cost)/(lnt+1) I found the equation of the tangent to be y=-x I've drawn the curve and it seems to match my answer at t = 0 If somebody could please confirm my answer or tell me if I'm making some kind of error in my calculation it would be appreciated. 1. Your answer is correct. 2. The answer in the text is nonsensical --- a) it is not any kind of equation for a line, just a number for any fiven value of t, and b), it is not defined, even as a simple scalar, for t=0. I don't have that book. You present an excellent case against acquiring, or using, it. 1 Link to comment Share on other sites More sharing options...
the tree Posted October 31, 2011 Share Posted October 31, 2011 This does happen, text books are fallible. But that is a pretty awful failing, I'd concur with DrRocket. 1 Link to comment Share on other sites More sharing options...
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