I. Let z = f( x,y) = xy² Find the equation of the tangent when x = 1, y = 2 Find the equation of the linear approximation to f at (1,2) Find the equation of the tangent to f(x,y) = 4 at (1,2) Compute the total differential df. Find df at (1,2)

Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

Q: 5. In rectangular coordinates verify that V · V x A = 0 where A = xyz(ê+ ŷ + 2) by carrying out the…

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Q: How many horizontal tangent lines does the curve parametrized by the equations z(t) =-4t-1,…

A: on doing derivative we get the 1

Q: dy −2r — 9 (a) Show that = dx x + 2y (b) Find the two points where the curve given by the original…

A: Given- Consider the equation x2 + xy + y2 = 19.  To find-  Show that dydx = -2x - yx + 2y.  Find…

Q: ind the slope of the line that is tangent the curve sin(2x)+sin y=e*y – 1 at (0,0). our answer…

A:

Q: Find the equation for the curve f (x) at the point (x, y) meet the following conditions dy / dx = 4x…

A: A curve is a function with equation of the form y=f(x). A differential equation is an equation in…

Q: Consider the curve given by y² = 2 + xy. dy dx (a) Show that = 2y-x (b) Find all points (x, y) on…

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Q: Consider the curve 6+2xy + y³ = 4 The equation of the tangent line to the curve at the point (1, 1)…

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Q: A cardioid is given by the equation x² + y² = (2x²+2y²-x)². Find the equation for the tangent line…

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Q: Find the equation of the tangent line to y : = y = 125 2x²–5x+3 at x = 2.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.