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SOLVED:The point P(1, 0) lies on the curve y = sin(10π/x) . (a) If Q is the point (x, sin(10π/x)) , find the slope of the secant line PQ (correct to four decimal places) for x = 2, 1.5, 1.4, 1.3, 1.2, 1.1, 0.5, 0.6, 0.7, 0.8, and 0.9 . Do the slopes appear to be approaching a limit? (b) Use a graph of the curve to explain why the slopes of the secant lines in part (a) are not close to the slope of the tangent line at P . (c) By choosing appropriate secant lines, estimate the slope of the tangent
SOLVED:The point P(1, 0) lies on the curve y = sin(10π/x) . (a) If Q is th…
Jul 9, 2021
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The point P(0.5,0) lies on the curve y=cosπx . (a) If Q is the point (x, cosπx), use your calculator to find the slope of the secant line P Q (correct to six decimal places) for the following values of x : (i) 0 (ii) 0.4 (iii) 0.49 (iv) 0.499 (v) 1 (vi) 0.6 (vii) 0.51 (viii) 0.501 (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(0.5,0) . (c) Using the slope from part (b), find an equation of the tangent line
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