At what points (x,y,z) in space are the functions continuous? a. h(x,y.z) = In (3z° - 4x- 5y- 4) 1 b. h(x.y,z) = z° - Vx+y a. At which points is h(x,y,z)= In (3z- 4x-5y- 4) continuous? Choose the correct answer below. O A. All points satisfying 3z-4x2 5y-4 O B. All points satisfying x y#z O C. All points satisfying 3z - 4x-5y<4 O D. All points satisfying 3z-4x- 5y> 4 O E. All points except (0,0,0) OF. All points satisfying 3z O H. No points - 4x - 5y 4 O G. All points 1 b. At which points is h(x,y.z) = continuous? Choose the correct answer below. 22 - x+y O A. All points satisfying x+ y20 O B. All points satisfying z' x +y O C. All points satisfying z> x+y O D. All points satisfying x# y#z O E. All points satisfying x+ y> 0 OF. All points satisfying x+y20 and z # Vx+y O G. All points O H. No points

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: