4.26) my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text. L'Hospital's rule 4.26. Prove L'Hospital's rule for the case of...

4.26) my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.


Extracted text: L'Hospital's rule 4.26. Prove L'Hospital's rule for the case of the "indeterminate forms" (a) 0/0 and (b) ∞/0. (a) We shall suppose that f(x) and g(x) are differentiable in a <>

Extracted text: Assume x, is such that a < xo=""><>< e.="" keeping="" x,="" fixed,="" we="" see="" that="" 1-8(x,)/g(x)="" lim="" |="1" since="" 1="" lim="" f(x),="∞" and="" lim="" g(x)="0" 1-f(x,)/f(x)="" xxo="" +="" xxo="" +="" x-xo="" +="" then="" taking="" the="" limit="" as="" x="" →="" xo+="" on="" both="" sides="" of="" (2),="" we="" see="" that,="" as="" required,="" f(x)="" f'(x)="L" =="" lim="" lim="" x→xq+="" g(x)="" x-="">Xo+ g'(x) Appropriate modifications of this procedure establish the result if x → xo -, x → Xo, x →∞, or x → -.