I want to know HOW to do these, not just the answers. In fact, I\'d rather you t

Question

I want to know HOW to do these, not just the answers. In fact, I'd rather you tell me what to do and why and give me no answer than just the answer. Thank you. 1) Suppose the line 2x -y + 1 = 0 is tangent to the level curve f(x,y) = 2 at the point (0,1). Determine which of the vectors below is parallel to ?f(0,1). a. i + 2j b. 2i + j c. i - 2j d. -2i + j e. i + j f. none of these 2) Find the curvature at t = 0 of the curve described by x = 2 - cost(t), y = ?(sin(t)), z = cos(t) a. 0 b. 1/3 c. 1/2 d. 1/?2 e. ?2 f. none of these

Explanation / Answer

2x -y + 1 = 0 is tangent to the level curve f(x,y) = 2 at the point (0,1) so they hold a relation (slope of tangent line)*(slope of line)=-1 slope of 2x -y + 1=0 is 2,hence slope of f(x,y) at (0,1) is -1/2 slope 0f ai+bj is b/a... so the answer is (d)-1/2 curvature at t=0, curvature= || f'(t) x f''(t) || / ||f'(t)||

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