Suppose we are given F. dr = 1 and | F • dr = −3. Calculate • dr given that ♬ C₁ is conservative (locally) on the domain between C and the curves C₁, C₂. Is F conservative on R2? Explain.

Q: Consider the point (x, y) lying on the graph of y = 2x - 3. Let L be the distance between the points…

A: Given,

Q: Which of the following expressions does NOT make sense?

A:

Q: 9. Determine an expression for the gradient of f =Y x+y

A:

Q: Let P = (x,y) be a point on the graph of y = x- 12. %3! Express the distance, d, from P to the…

A: The given problem is to find the distance function in terms of x where distance between origin and…

Q: Consider the point (x,y) lying on the graph of the line 8x + 7y = 3. Let L be the distance from the…

A: We use the distance formula

Q: Find the slope in the x-direction at the point P(0, 2, f(0, 2)) on the graph of f when f (x, y) 3(y?…

A:

Q: Consider an F-curve with d f = (2, 14). Determine F0.05.

A: The F-curve 0.05 area with degrees of freedom 2 and 14.

Q: 1. Let f (x, y) = 3+ /1+x – y² a. Find f(0,0) b. Find the range of f. c. Find and sketch the domain…

A:

Q: Use the contour diagram of f to decide if the specified directional derivative is positive,…

A:

Q: Let f(x) =4x divided by x -3. Find the slope of the secant lines on the graph of F through P(5, 10)…

A: f(x)=4x/(x-3) P(5,10) and Q (6, a)  (say) a= f(6)= 24/3 =8  Q(6,8) is

Q: Use the contour diagram of f to decide if the specified directional derivative is positive,…

A: From the Contour diagram, the required function is  f(x,y)=x2+y2 The gradient of f is given as…

Q: 1. Consider the function z = f(x,y) = x2 –- 2x + 3y? + 6y. i. State its domain. ii. Find the range…

A: Given, z=f(x,y)=x2-2x+3y2+6y

Q: Let P= (x,y) be a point on the graph of y = x. Express the distance, d, from P to (7,0) as a…

A: