Did the germans archeive their goal of capturing paris in their march 1918 offensive? why or why not?

IN their last spring offensive of 1918, also known as Kaiserschlacht (Kaiser's Battle) or Ludendorf f Offensive, the German Imperial Army poured all its resources, including troops recently freed from the Eastern Front as a result of the Russian capitulation, and came close to achieve its goal of taking Paris in order to force the Western Allies to negotiate advantageous peace terms to Germany before the United States flooded the battlefields with men, equipment and supplies.

On March 21, 1918. the Germans launched four simultaneous offensives along the western Front:  Operations  Michael, Georgette, Blücher-York and Gneisenau. Their goal was to run over the Allied troops through the extensive use of assault troops leading the attack of the regular troops. Assault troops (Stosstruppen in German) developed special tactics using small numbers of troops in order to infiltrate through the enemy lines, open corridors through the barbed wire and selectively eliminate machine gun nests and snipers. allowing the bulk of the regular troops to easily assault and take the enemy's first lines of defense.

Operation Blücher-York came as close to Paris as the Marne Offensive of 1914, but a worsening lack of supplies and heavy casualties sustained by the Germans prevented them from achieving their main goal of crushing the enemy forces in order to force the Allied powers to negotiate peace in spite of a relatively large gain of territory. By July 18, the Spring Offensive was ordered to an end by the German High Command, and the arrival of a great number of fresh U.S. troops the next month decisively turned the tide of the war on the Allied side.

A

The reciprocal of the slope of f(x) is the same as the slope of f–1(x).

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