Let and be two variable straight lines

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let (tan⁡α)x+(sin⁡α)y=α(\tan\alpha)x+(\sin\alpha)y=\alpha and (αcsc⁡α)x+(cos⁡α)y=1(\alpha\csc\alpha)x+(\cos\alpha)y=1 be two variable straight lines, where α\alpha is the parameter. Let PP be their point of intersection. In the limiting position, as α→0\alpha\to0, the point of intersection is (1) (2,−1)(2,-1) (2) (2,1)(2,1) (3) (−2,1)(-2,1) (4) (−2,−1)(-2,-1)

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