QuestionEstimate $y$ at $x=3.1$ using the tangent line of the curve $x^{3}+x \tan y=27$ at $(3,0)$. Choose from (A) -2.7 (B) -0.9 (C) 0 (D) 0.1 (E) 3.0.

Studdy Solution
Calculate the estimated value of $y$.
$$y = -9(3.) +27 = -0.9$$The estimated value of $y$ at $x=3.$ is -0.9, so the correct answer is (B) -0.9.