. Is f(x)= Vx + 1 continuous at x == -1? Yes, because all functions are continuous No, because the limit of f(x) does not exist. Yes, because its limit is 0
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- Let f(x, y) = xy /(x 2 + y2). Show that f(x, y) approaches zero along the x- and y-axes. Then prove that lim f(x, y) does not exist by (x,y) (0,0)showing that the limit along the line y =xis nonzero.For the attatched functions, either find the limit at (x, y) = (0, 0), or show that the limit doesn't exist.Evaluate the limit. limit of (x + sin 1/x)^1/x as x approaches positive infinity
- Let f (x, y) = xy/(x2 + y2). Show that f (x, y) approaches zeroalong the x- and y-axes. Then prove that lim (x,y)→(0,0)f (x, y) does not exist by showing that the limit along the line y = x is nonzero.consider a function f, defined by f(x,y) = -y/√x2+y2 what is the behavior of f along the line y=x when x>o; that is, what is the value of f(x,x) when x>0? If we approach (0,0) by moving along the line y=x in the first quadrant(thus considering f(x,x) as x→0+, what value do we find for the limit?