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Consider the curve defined by the equation 5 + x² * sqrt(y - 2) = y² - x * [lim(t->0) tan(3t)/t] - 5x * [lim(t->0) sin(t)/t], where [.] denotes the greatest integer function. Find the equation of the normal to this curve at the point (1, 3).

1. 2x + 3y = 11
2. 8x - 3y = -1
3. 11x + 10y = 41
4. 13x + 6y = 3

Correct answer: 11x + 10y = 41

Solution

After evaluating the limits, the curve becomes 5 + x²*sqrt(y-2) = y² - 3x. Implicit differentiation at (1,3) gives dy/dx = 10/11, so the normal has slope -11/10, leading to 11x + 10y = 41.

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