Science:Math Exam Resources/Courses/MATH200/April 2012/Question 02 (a)
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Question 02 (a) 

Let Use a linear approximation of the function z=f(x,y) at (0,1) to estimate f(0.1,1.2). 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The linear approximation to a multivariable function ƒ(x,y) at a point (x,y) = (a,b) is given by L(x,y) where where the subscripts denote partial differentiation with respect to the given variable. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The linear approximation to a multivariable function ƒ(x,y) at a point (x,y) = (a,b) is given by L(x,y) where where the subscripts denote partial differentiation with respect to the given variable. In this case the partial derivatives of are and we wish to approximate ƒ near (x,y) = (0,1). Hence the linear approximation we seek is: Using the linear approximation, we can estimate the value of ƒ(0.1,1.2) as 