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求曲线x=cost+cos的平方t,y=1+sint,上对应于t=派/4的点处的法线斜率.答案为什么是根号2+1
人气:339 ℃ 时间:2020-05-12 10:31:57
解答
x'(t) = -sint + 2cost(-sint) = -sint - sin2t
y'(t) = cost
t= π/4点处的切线斜率k = y'(t)/x'(t)
t= π/4点处的法线斜率k' = -1/k = -x'(x)/y'(t) = (sint + sin2t)/cost = (√2/2 + 1)/(√2/2) = √2 + 1
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