Question

Find \(lt_{(x,y,z)\rightarrow(2,2,4)}\frac{x^2+y^2-z^2+2xy}{x+y-z}\)

(a) ∞

(b) 123

(c) 9098

(d) 8

This question was posed to me in class test.

My enquiry is from Limits and Derivatives of Several Variables topic in portion Partial Differentiation of Engineering Mathematics

Answer 1

The correct choice is (d) 8

The explanation: Simplifying the expression yields

\(lt_{(x,y,z)\rightarrow(0,0,0)}\frac{(x+y)^2-z^2}{(x+y)-z}\)

\(lt_{(x,y,z)\rightarrow(0,0,0)}\frac{(x+y+z).(x+y-z)}{(x+y-z)}\)

\(lt_{(x,y,z)\rightarrow(0,0,0)}(x+y+z)=2+2+4\)

=8