Question

Question 1. 30% Given the function f(x, y) = e 1. Specify the domain and range of f. 2. Describe the level curves off and graph the one that passes through the point (2,4). 3. Find the limit, if possible, when (x,y) approaches (0,0) of the function f(x,y). 4. Find the equation of the tangent plane and the normal line to surface defined by at the point (1,1,e). 5. We now let x = 12 and y = In 3t use the chain rule to find

Answer 1

1. As x is a divisor, x≠0

And as y lies inside a square root, y is non negetive.

Hence domain of the function is {(x, y) :x≠0 & y≥0}

And as exponent is always greater than zero. The range of the function is {x:x>0}

Tayo 2. let pa vagy log a [ase] y = x²(log a) and note that nto, yota md rasuloga, Hence n to for all and nyo for axı. e. It is a half parabola. with vertex at (0,0) and arxis of the porrabola is yoniga we and the get the left half of parabola for a 71 we get right half of the parabola,