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.(a) Consider a function h(u,v)=4u^2+4v^2+1. Find the level curves for k=n+1,n+2,n+3,n+4,n+5,n+6,n+7.Where n is your arid number (for example if your arid number is 19-arid-12345 then choose n=12345). Perform all steps clearly in detail. Also Sketch the neat Graph. (3 points) (b) Let u=f(v),where f(v)=b(v^2-2v) draw the graph for different values of b∈[-5,5]. Just imagine that the values of b lies on the axis which is perpendicular to the laptop screen. Explain the behavior of graph when we change the values of b by assuming that b denotes the graph distance in back or in front of laptop screen? Also explain about the shape of graph (how it look like)? What are the necessary conditions for different types of functions to be defined in two variables explain with examples? How the conditions affect the input and output variables?
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