Question 1

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The temperature on an anisotropic rectangular slab is given by the function

T left parenthesis x comma y right parenthesis equals fraction numerator 45 times y over denominator x squared plus y squared plus 1 end fraction

a) The temperature's rate change at the point (1,2) on the direction open square brackets fraction numerator square root of 10 over denominator 10 end fraction comma fraction numerator 3 times square root of 10 over denominator 10 end fraction close square brackets is


b) Employing the concept of the differential, calculate the temperature at the point (0.99,2.005) (with all decimal values)



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