Question:
Let f : \(\R^3 → \R\) be defined as f(x, y, z) = x3 + y3 + z3 , and let L : \(\R^3 → \R\) be the linear map satisfying
\(\lim\limits_{(x,y,z)\rightarrow(0,0,0)}\frac{f(1+x,1+y,1+z)-f(1,1,1)-L(x,y,z)}{\sqrt{x^2+y^2+z^2}}=0.\)
Then L(1, 2, 4) is equal to ____________. (rounded off to two decimal places)
Let f : \(\R^3 → \R\) be defined as f(x, y, z) = x3 + y3 + z3 , and let L : \(\R^3 → \R\) be the linear map satisfying
\(\lim\limits_{(x,y,z)\rightarrow(0,0,0)}\frac{f(1+x,1+y,1+z)-f(1,1,1)-L(x,y,z)}{\sqrt{x^2+y^2+z^2}}=0.\)
Then L(1, 2, 4) is equal to ____________. (rounded off to two decimal places)
\(\lim\limits_{(x,y,z)\rightarrow(0,0,0)}\frac{f(1+x,1+y,1+z)-f(1,1,1)-L(x,y,z)}{\sqrt{x^2+y^2+z^2}}=0.\)
Then L(1, 2, 4) is equal to ____________. (rounded off to two decimal places)
Updated On: Oct 1, 2024
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Correct Answer: 20.99 - 21.01
Solution and Explanation
The correct answer is 20.99 to 21.01.(approx)
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