Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

Q: an equation of the line tangent to the function of x2 + (y – x)2 = 9 at x = 1.

A: At given value of x find y Differentiate at given value Use equation of tangent line

Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

A:

Q: For the curve f (x) = -2(3)" +3, the y-intercept occurs at:

A: We know that as y intercept x=0.

Q: Find the tangent plane to the graph of f(x, y) = x² + y² + 4x - 2y +1 at the point (0,0,1).

A:

Q: Find all points on the graph of x2y − 2x + 63y = 2 where the tangent line is horizontal. (Enter…

A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

Q: Let z = (1+z)√√/50 — x² − y². - (A) Calculate the equation of the tangent plane at x = 3, y = 4. (B)…

A: z = (1 + x)50 - x2 - y2 The given function is of the form z = f(x) To calculate the equation of the…

Q: Let y = f(x) be defined parametrically as y=t+tt, x = 2t -t, te R. Find f(x) and discuss its…

A:

Q: Let f(x) = x² + 2x+1 a) Find the equation of the secant line between the points P and Q on the graph…

A: Let (a) To find the equation of the secant line between the points P and Q on the graph of , where P…

Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

A:

Q: Evaluate f (5ydy + 3xydx) C if C is the closed curve determined by the x-axis, the parabola y = x²…

A:

Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

A:

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

A:

Q: Determine the stationary point of the curve y=x-In(1+x).

A:

Q: Show the curve y(u) = o(u, 1) represents a meridian (line of longitude) on S², while the curve y(v)…

A: Given Information:The curve  and the curve  on .To show:The curve  represents a meridian (line of…

Q: Find for the curve dx In (2x) + 5xy + y = 3.

A:

Q: Find the points on the curve z t? – 10t – 8, y = t² + 4t + 6 that have: A. a horizontal tangent line…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Find the speed of the curve 7 (t) = (5t2 + + 6, 7t + 1, t³ + 8t) at t = 4 Бpeed

A: Magnitude of the velocity is speed

Q: Tangents are drawn to x² + y² = 1 from any arbitrary point P on the line 2x + y - 4 = 0. The…

A: Tangents are drawn to x2+y2=1 from any arbitrary point P on the line 2x+y−4=0. We have to find the…