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For x>0, define L(x)=∫1xt1dt. (keep in mind that we require x be positive so that the FTC applies and the function, L(
Posted: Thu Jul 14, 2022 4:41 pm
by answerhappygod
- For X 0 Define L X 1x T1 Dt Keep In Mind That We Require X Be Positive So That The Ftc Applies And The Function L 1 (35.61 KiB) Viewed 39 times
For x>0, define L(x)=∫1xt1dt. (keep in mind that we require x be positive so that the FTC applies and the function, L(x), is both continuous and differentiable). Using this definition and properties of the integral prove the following: a. L(1)=0. b. L′(x)=x1 for every x>0. c. L(ab)=L(a)+L(b) for every a,b>0.