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question:Let (a in mathbb{R}), and the function (f(x) = e^x + frac{a}{e^x}) has a derivative (y = f'(x)) that is an odd function. If the slope of a tangent line to the curve (y = f(x)) is (frac{3}{2}), then the abscissa of the tangent point is ( ). A: (frac{ln 2}{2}) B: (-frac{ln 2}{2}) C: (ln 2) D: (-ln 2)
answer:Given that (f'(x) = e^x - frac{a}{e^x}) is an odd function, (∴ f'(0) = 1 - a = 0) (∴ a = 1), (f(x) = e^x + frac{1}{e^x}), (f'(x) = e^x - frac{1}{e^x}), Since the slope of a tangent line to the curve (y = f(x)) at point ((x, y)) is (frac{3}{2}), (∴ frac{3}{2} = e^x - frac{1}{e^x}), Solving the equation yields (e^x = 2), (∴ x = ln 2). Therefore, the correct choice is: (boxed{C}). This problem mainly examines the definition of the derivative of a function and the arithmetic operations of derivatives, as well as the properties of functions' odd and even nature, and the geometric meaning of derivatives: the derivative at a point is the slope of the tangent line at that point. It involves basic knowledge and simple application, with a low level of difficulty.
question:What type of details about hubert lacroix can be gathered from the following bio? Bio: hubert t. lacroix -lrb- born july 13 , 1955 -rrb- is a canadian lawyer and the president and ceo of the canadian broadcasting corporation -lrb- cbc -rrb- , the national public radio and television broadcaster . born in montreal , quebec , lacroix attended collège jean-de-brébeuf before receiving a bachelor of law degree from the mcgill university faculty of law in 1976 . he was admitted to the quebec bar in 1977 and received a master of business administration from mcgill in 1981 . he started practising law with the firm of o'brien , hall , saunders in 1977 . a senior adviser with the law firm stikeman elliott llp , he was executive chairman of telemedia corporation from 2000 to 2003 . he has been a member of the board of directors of zarlink semiconductors since 1992 . he also sat on the boards of donohue inc. , circo craft co. . inc. , adventure electronics inc. and michelin canada inc. . lacroix is an associate professor with the faculty of law at université de montréal where he teaches in the securities , and mergers and acquisitions . he was a basketball colour commentator on télévision de radio-canada during the 1984 , 1988 , and 1996 summer olympics . he was also a weekly contributor for radio-canada 's hebdo-sports radio show . his recent time in the oasis montreal half-marathon was 1:32:41.0 . he was appointed president and ceo of the cbc , effective january 1 , 2008 , by prime minister stephen harper in november 2007 replacing robert rabinovitch.lacroix was re-appointed for a second term , on october 5 , 2012 . Answer:
answer:1. Hubert Lacroix was born on July 13, 1955. 2. He is a Canadian lawyer. 3. Lacroix serves as the President and CEO of the Canadian Broadcasting Corporation (CBC), which is the national public radio and television broadcaster. 4. He was born in Montreal, Quebec. 5. Lacroix attended Collège Jean-de-Brébeuf. 6. He received a Bachelor of Law degree from McGill University Faculty of Law in 1976. 7. Lacroix was admitted to the Quebec Bar in 1977. 8. He obtained a Master of Business Administration from McGill in 1981. 9. Lacroix began practicing law with the firm of O'Brien, Hall, Saunders in 1977. 10. He was a senior adviser with the law firm Stikeman Elliott LLP. 11. Lacroix served as Executive Chairman of Telemedia Corporation from 2000 to 2003. 12. He has been a member of the board of directors of Zarlink Semiconductors since 1992. 13. Lacroix has served on the boards of Donohue Inc., Circo Craft Co. Inc., Adventure Electronics Inc., and Michelin Canada Inc. 14. He is an associate professor at the Université de Montréal Faculty of Law, teaching in securities and mergers and acquisitions. 15. Lacroix worked as a basketball colour commentator during the 1984, 1988, and 1996 Summer Olympics for Télévision de Radio-Canada. 16. He was a weekly contributor for Radio-Canada's Hebdo-Sports radio show. 17. Lacroix participated in the Oasis Montreal half-marathon with a time of 1:32:41.0. 18. Appointed as President and CEO of CBC on January 1, 2008, by Prime Minister Stephen Harper, replacing Robert Rabinovitch. 19. Lacroix was re-appointed for a second term on October 5, 2012.
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answer:I understand the request and will comply. Here is my response: I can provide you with information or assistance on various topics without using the forbidden words. Please let me know what you need help with.
question:I'm thrilled to share some exciting insights from the Annual National Conference on Autism Spectrum Disorder in Boston! One of the most compelling sessions I attended was on Interactive Storytelling as a therapy method for children with ASD. This technique leverages the power of narratives to improve communication skills and social interaction, and I'm eager to integrate it into my practice. One of the most rewarding moments in my career was recently with a young client, Jake, and his family. Over the past year, Jake has made incredible progress in his communication and social skills. His parents and the multidisciplinary team, including occupational therapists and educators, have been instrumental in his journey. Seeing Jake's confidence grow and witnessing the joy in his family's eyes has been truly heartwarming. For those of you who work with children on the spectrum or are part of a supportive network, I encourage you to explore interactive storytelling as a tool. Let's continue to share best practices and support each other in making a difference in the lives of our young clients and their families. 🌟 #AutismAwareness #SpeechTherapy #ChildDevelopment #TherapeuticSuccess #InteractiveStorytelling
answer:Excited to share insights from the Annual National Conference on Autism Spectrum Disorder in Boston! A standout session was on Interactive Storytelling as a therapy for children with ASD, enhancing communication and social skills. I plan to incorporate this method into my practice. A highlight of my career was seeing Jake, a young client, make remarkable progress in communication and social skills over the past year. His growth, supported by his parents and a multidisciplinary team, has been incredibly rewarding. For those working with children on the spectrum, consider exploring interactive storytelling. Let's share best practices and support each other in making a positive impact. 🌟 #AutismAwareness #SpeechTherapy #ChildDevelopment #TherapeuticSuccess #InteractiveStorytelling