June 21st, 2019, 05:18 PM  #1 
Newbie Joined: Jun 2019 From: india Posts: 1 Thanks: 0  find range of the function
f(x)=cosx(sinx+(sin^2x+sin^2y)^1/2)

June 22nd, 2019, 10:46 AM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 309 Thanks: 160 
Is y a constant, or is the function f(x,y)? Either way, "Find the range," can be treated as, "Find the minima/maxima." Find df/dx and df/dy (if a 2D function) and set them equal to zero. To simplify it, we can tell that both the minimum and maximum will be at sin^2y = 1 if y is variable. We also know that the range will definitely be smaller than +/(1+sqrt(2)), so you can check your answer against that. Also, you can plot f(x,y) over [pi,pi]x[pi,pi] to check your answer. (Or just f(x,pi) for pi <= x <= pi, using the observation above.) 

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