MTH109 Tutor-Marked Assignment 1 This project is price 10% of the final effect for MTH109 Calculus. The decrease-off date for this project is 05 March 2026, 2355hrs. Sing to Students: It’s most likely you’ll perchance also very properly be to contain the following particulars for your submission: Course Code, Title of the TMA, SUSS PI No., Your Establish, and Submission Date. As an illustration, ABC123 TMA01 Sally001 TanMeiMeiSally (leave out D\/O, S\/O). Exhaust underscore and no longer home. Demand 1 Resolve the following limits. Demand 2 The Air Quality Health Index (AQHI) is a scale from 1 to 11 that is venerable to discuss the stage of properly being possibility linked with air quality. A sample of 647 readings of air air pollution taken at a monitoring speak over a effect duration is venerable to calculate 647 values of the AQHI. Desk Q2 presentations the frequency counts of every price of the AQHI essentially based completely completely on these readings. Given a sample X 1 ,\u2026,Xn of n observations of the AQHI, the (uncorrected) sample variance s 2(\u00b5) relative to a parameter \u00b5 is given by n s 2(\u00b5) = 1n \u00a0 i\u2211=1(Xi \u2212\u00b5)2 . AQHI 1 2 3 4 5 6 7 8 9 10 11 Frequency 0 38 197 206 152 47 7 0 0 0 0 Desk Q2: Frequency counts of AQHI values. (a) Put together spinoff exams by differentiating with appreciate to \u00b5 to point to that s 2(\u00b5) is minimised when 1 n \u00b5 = X = n i\u2211=1Xi , the sample mean. (10 marks) (b) Calculate the discover of the sample variance s 2(X) for the AQHI data in Desk Q2, giving your reply honest to 2 decimal locations. (5 marks) Demand 3 (a) Outline a aim f : R \u2212\u2192 R by the establish a and b are genuine constants. (i) Resolve the variety of values of a and b such that f is continuous at x= (5 marks) (ii) The exhaust of the restrict definition of differentiability, resolve the variety of values of a and b such that f is differentiable at x = (10 marks) (b) A rectangular sheet of paper OACB is folded over so that the nook O correct reaches a point P on the side AC as proven in Resolve Q3b. Let OA = a and OB = b, the establish 0 < a < b, and let x = AP. As P strikes from A to C, the sq. of the length of the crease shaped by the fold is given by the aim L 2(x) : [0,b] \u2212\u2192 R defined by \u00a0 (i) Resolve whether the aim L 2(x) is continuous over [0,b]. (5 marks) (ii) Resolve the variety of values of a and b, self-discipline to 0 < a < b < \u221e, such that the aim\u221a L 2(x) has a unusual most over [0,b] at x = b\u2212\u00a0\u00a0\u00a0\u00a0\u00a0 b 2 \u2212a 2. (10 marks) Demand 4 (a) Demonstrate that the tangent line to the graph of the equation y 2 =x 3 on the purpose 8\/9, 16\u221a2\/27 is additionally a popular to the graph one day. (5 marks) (b) Demonstrate that the tangent traces to the graph of the equation y 2(x\u22121) = x 2(x+1) on the components the establish x = 2 intersect at an attitude of . (3 marks) Demand 5 END OF ASSIGNMENT\n<\/p>\n","protected":false},"excerpt":{"rendered":"
MTH109 Tutor-Marked Assignment 1 This project is price 10% of the final effect for MTH109 Calculus. The decrease-off date for this project is 05 March 2026, 2355hrs. Sing to Students: It’s most likely you’ll perchance also very properly be to contain the following particulars for your submission: Course Code, Title of the TMA, SUSS PI […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-30028","post","type-post","status-publish","format-standard","hentry","category-solutions"],"_links":{"self":[{"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/posts\/30028","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/comments?post=30028"}],"version-history":[{"count":0,"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/posts\/30028\/revisions"}],"wp:attachment":[{"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/media?parent=30028"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/categories?post=30028"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/tags?post=30028"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}