For the function f(x, y) = 5e³ sin(y), find a unit tangent vector to the level curve at the point (-5,3) that has a positive a component. Present your answer with three decimal places of accuracy.

Q: Find the gradient of the tangent line to y when x = 2.

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Q: Determine the equation of the line that is tangent to y= ex / x2 at x=2.

A: The given function is, y=exx2 To find the line that is tangent to y=exx2 at x=2.

Q: 3. Find the equation of the tangent line to the graph of x²y? + 9xy = 162 at the point (-3, 6).

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Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope -12 at x = -1, and…

A: To find a parabola with equation.

Q: (6) Consider the differential equation: y" – 6y' + 9y = f(x) a) Find the solution to the homogeneous…

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Q: On the same axes, plot the curve y = 1x, the line y = x/8, and the tangent line to y = 1x that is…

A: Given curve is y=x. Let x,y be any point on the curve. Differentiate function with respect to x.…

Q: Find an equation of the line tangent to the curve defined by æ° + 2xy + y% = 104 at the point (2,…

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Q: State the rule that has to be applied first in order to differentiation the function y = -5te2t. a.…

A: We have a function y = -5te2t . Now we need to find which rule needs to be applied first to…

Q: (c) Find an equation of the tangent line to the graph of x2/3 + y2/3 = 5 at the point (1,8).

A: Given: The equation of the graph is  x23 + y23 = 5 To find: The equation of the tangent line to the…

Q: c) the equation of the tangent for y=xlnx at the point where x = e

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Q: Find an equation of the tangent line to the curve y = x/x that is parallel to the line y = 6 + 3x. y…

A: The given question has been solved in detail

Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: 2. Find the equation of the tangent line to the curve. x=3t²+8t, y=2t²³-4t, whent=-2.

A: To find out the equation of the tangent line to the given curve when t=-2.

Q: Determine the equation of the line tangent to y = x + tan x at the point (T, T).

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