Mathematics, 07.12.2021 22:20 vDxrk
1+(f′(x))^2−f′′(x)=0
Make the substitution u=f′ in equation (B). Solve the resulting first-order equation for u(x).
Integrate your answer for problem 1 to find f(x) solving the original Euler-Lagrange equation.
What is the cheapest path from (−1,0) to (1,0)?
What happens when you try to use the formula you found in problem 2 to write out the cheapest path from (−3,0) to (3,0)?
Explain why the formula doesn't work in problem 4 in terms of the original problem of finding a cheapest path.
Answers: 2
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Write the sine and cosine values of a, b, respectively, in the figure for (1) and (2) + explanation.
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What is the range of the function? f(x)=-2|x+1|? a. all real numbers. b. all real numbers less than or equal to 0. c. all real numbers less than or equal to 1. d. all real numbers greater than or equal to 1
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1+(f′(x))^2−f′′(x)=0
Make the substitution u=f′ in equation (B). Solve the resulting first-order e...
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