Math  /  Calculus

QuestionFind the equation of the tangent line at the given point on the curve. xsin(πy)=5;(5,4)x-\sin (\pi y)=5 ;(5,4)

Studdy Solution
Use the point-slope form of the equation of a line to find the equation of the tangent line. The point-slope form is:
yy1=m(xx1) y - y_1 = m(x - x_1)
where m m is the slope and (x1,y1) (x_1, y_1) is the point. Substitute m=1π m = \frac{1}{\pi} and (x1,y1)=(5,4) (x_1, y_1) = (5, 4) :
y4=1π(x5) y - 4 = \frac{1}{\pi}(x - 5)
The equation of the tangent line is:
y=1πx5π+4 y = \frac{1}{\pi}x - \frac{5}{\pi} + 4

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