4- Test the continuity of following at (0, 0) and if di type of discontinuity. fx.y) y + 0 (i) 0, y = 0 (г.у) + (0,0) f(x,y) (ii) 0, (х.у) - (0,0)

Q: а) f.(x, y) b) f (x, у) ху 1 3 f (x, у) 16x4y4 Зу'х + 5ху

A: Consider the given function

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A: The given function is: z=fx,y=-4x3-6y2-7xy   As we know that; The Power Law: ddxxn=nxn-1

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A: Letandfind the derivative

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.