### [數學][問題]:微積分證明題..(-_-)..

#ed_op#DIV#ed_cl#let#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; f(x)=arctan(a+x/1-ax),x#ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl#≠1/a.#ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl#(a)show that f'(x)=a/(1+xx),x#ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl#≠1/a.#ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl#(b)show that there is no constant C such that f(x)=arctanx+C for all x#ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl#≠1/a.#ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl#(c)Find constants C1 and C2 such that#ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl#&nbsp;&nbsp; f(x)=arctanx+C1&nbsp; for x&lt;1/a#ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl#&nbsp;&nbsp;&nbsp;f(x)=arctanx+C2&nbsp;&nbsp;for x&gt;1/a.#ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl##ed_op#SPAN lang=ZH-CN style="FONT-FAMILY: SimSun; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'; mso-fareast-language: ZH-CN"#ed_cl#&nbsp;&nbsp;#ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#