YLL討論網

#ed_op#DIV#ed_cl#let#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#      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# #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#   f(x)=arctanx+C1  for x<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#   f(x)=arctanx+C2  for x>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#  #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#/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##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#