[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-463328-105":59,"doc-detail-463328-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","math-1a-midterm-1-practice-1","Math 1A Midterm 1 - Practice 1","","Math 1A Midterm 1 (Practice 1) by Professor Paulin provides five graded problems focused on core calculus skills. Tasks include finding domains of algebraic, trigonometric, and logarithmic functions, transforming graphs using function operations, evaluating an arctangent expression with exact values, computing several limits via limit laws and continuity checks using epsilon-delta methods, and applying the direct definition of the derivative for a radical function, including tangent-line verification.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/math-1a-midterm-1-practice-1/463328/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/math-1a-midterm-1-practice-1/463328.png","ImageObject",300,407,{"name":92,"@type":93},"นรินทร์","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-09-30",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What restrictions are stated for the exam (e.g., calculators)?","Question",{"text":112,"@type":113},"Calculators are not permitted. Students must stay until the exam is complete and write solutions neatly in the provided spaces.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What topics are covered in Question 1 and Question 2?",{"text":117,"@type":113},"Question 1 asks for domains of given functions. Question 2 describes how to draw a transformed graph starting from y = f(x).",{"name":119,"@type":110,"acceptedAnswer":120},"How does Question 4 test continuity at x = 0?",{"text":121,"@type":113},"Question 4 requires an ε, δ proof showing the given function is not continuous at x = 0 using the formal definition.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},463328,1791045009,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},2336475104957,"https://ap-avatar.wpscdn.com/avatar/22000c4c6bd8a5076e1?x-image-process=image/resize,m_fixed,w_180,h_180&k=1787554080175789136","MATH 1A MIDTERM 1 (PRACTICE 1) PROFESSOR PAULIN  \n\n| DO NOT TURN OVER UNTIL INSTRUCTED TO DO SO . |\n| --- |\n| CALCULATORS ARE NOT PERMITTED |\n\nYOU MAY USE YOUR OWN BLANK PAPER FOR ROUGH WORK  \nSO AS NOT TO DISTURB OTHER STUDENTS, EVERYONE MUST STAY UNTIL THE EXAM IS COMPLETE  \nREMEMBER THIS EXAM IS GRADED BY A HUMAN BEING . WRITE YOUR SOLUTIONS NEATLY AND COHERENTLY, OR THEY RISK NOT RECEIVING FULL CREDIT  \nTHIS EXAM WILL BE ELECTRONICALLY SCANNED . MAKE SURE YOU WRITE ALL SOLUTIONS IN THE SPACES PROVIDED . YOU MAY WRITE SOLUTIONS ON THE BLANK PAGE AT THE BACK BUT BE SURE TO CLEARLY LABEL THEM  \nName and section:    \nGSI’s name:    \nMath 1A Midterm 1 (Practice 1)  \nThis exam consists of 5 questions. Answer the questions in the  \nspaces provided.  \n1. Determine the domains of the following functions:  \n(a) (10 points)  \n√ 1 − x2  \ntan2 (x) − 1  \nSolution:  \n(b) (15 points)  \nln(sin(2x) + 1)  \nSolution:  \nPLEASE TURN OVER  \n2. (a) (15 points) Describe in words, how, starting with the graph y = f(x) , one can draw the graph  \n2 − x  \ny = −3f( ) + 1.  \n3  \nSolution:  \n(b) (10 points) Give the precise value of the following:  \n19π  \narctan(tan( ))  \n6  \nSolution:  \nPLEASE TURN OVER  \n3. (25 points) Calculate (using the limit laws) the following limits. If a limit does not exist determine if it is ∞ , −∞ or neither.  \n(a)  \nlim sin(π(x2 + 1))  \nx→0  \nSolution:  \n(b)  \n x2 − x − 6  \nx2 x2 + 4x + 4  \nSolution:  \nPLEASE TURN OVER  \n(c)  \n1 −√x lim arccos(  )  \nx→ 1 1 − x  \nSolution:  \n(d)  \n2x + 7 x √ x2 + 9  \nSolution:  \nPLEASE TURN OVER  \n4. (25 points) Prove, using ϵ , δ methods, that the following function is not continuous atx = 0:  \nf (x) = !01  \nif x  0 if x = 0  \nPLEASE TURN OVER  \n5. (a) (15 points) Using the direct definition of the derivative to calculate the derivative of the function  \nf (x) = √2 − x.  \nWhat is the domain of the f′(x)?  \nSolution:  \n(b) (10 points) Show that the line y = −~~ x~~2~~+3~~ is a tangent line to some point on the graph y = f(x) .  \nSolution:  \nEND OF EXAM","cbCaieScCfSrDdzM","https://ap.wps.com/l/cbCaieScCfSrDdzM","pdf",112921,"English","# Instructions\n## Question 1: Domains of functions\n## Question 2: Graph transformation\n## Question 3: Exact value and limits setup\n## Question 4: ε-δ proof of discontinuity\n## Question 5: Derivative definition and tangent line","[{\"question\":\"What restrictions are stated for the exam (e.g., calculators)?\",\"answer\":\"Calculators are not permitted. Students must stay until the exam is complete and write solutions neatly in the provided spaces.\"},{\"question\":\"What topics are covered in Question 1 and Question 2?\",\"answer\":\"Question 1 asks for domains of given functions. Question 2 describes how to draw a transformed graph starting from y = f(x).\"},{\"question\":\"How does Question 4 test continuity at x = 0?\",\"answer\":\"Question 4 requires an ε, δ proof showing the given function is not continuous at x = 0 using the formal definition.\"}]","Math 1A Midterm 1 - Practice 1 | PDF",1790766407,18]