Let fg(x, y) = ln(x +(x^2 + y^2 )^(0.5)). (a) Find the domain of g. (b) Calculat

Question

Let fg(x, y) = ln(x +(x^2 + y^2 )^(0.5)). (a) Find the domain of g. (b) Calculate the derivative Du f in the direction of i + j. (c) Find the linear approximation of f around the point (3, 4)

Explanation / Answer

a) x+ (x^2+y^2)^0.5 > 0, for the function to be defined, assuming we take only the positivie root, the function is defined if x>0, and y belongs to R. b) derivative in the direction y= i+j is grad g. y. c) The best linear approximation at (3,4) will be y= mx+c where m= grad g at(3,4) and c can be found by substituting x=3, y=4 you can find def of gradient here(http://en.wikipedia.org/wiki/Gradient)

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