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A: Given:
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- Suppose F 1 and F 2 are both antiderivatives of f on an interval I How are F 1 and F 2 related?Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and estimate the error for h = 0.5 and h = 0.25 by (Error Estimation by Halving h).Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY
- If I let f be continuously differentiable on R^2, how do I prove that gradf = (fx,fy)?Determine two functions, defined on the interval ( − ∞ , ∞ ) , whose Wronskian is given by W ( f 1 , f 2 ) = e 2 x . Are the functions that you found linearly independent on ( − ∞ , ∞ ) ? How do you know?Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units of labor, y is the number of units of capital, andf(x, y) is the number of units produced. Use differentials to estimate the change in production if the number of units of labor is increased from 27 to 29 and the number of units of capital is increased from 64 to 67. What is the maximum production level if 4x + 2y = 13.