MTH109 Tutor-Marked Task 1 This assignment is fee 10% of the last sign for MTH109 Calculus. The closing date for this assignment is 05 March 2026, 2355hrs. Veil to Students: You are to incorporate the next particulars to your submission: Path Code, Title of the TMA, SUSS PI No., Your Title, and Submission Date. As an illustration, ABC123 TMA01 Sally001 TanMeiMeiSally (omit D\/O, S\/O). Exhaust underscore and never plan. Question 1 Resolve the next limits. Question 2 The Air Quality Successfully being Index (AQHI) is a scale from 1 to 11 that is outdated to communicate the stage of successfully being chance linked to air quality. A pattern of 647 readings of air pollution taken at a monitoring residing over a assign duration is outdated to calculate 647 values of the AQHI. Desk Q2 shows the frequency counts of every fee of the AQHI in step with these readings. Given a pattern X 1 ,\u2026,Xn of n observations of the AQHI, the (uncorrected) pattern 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) Apply derivative tests by differentiating with appreciate to \u00b5 to prove that s 2(\u00b5) is minimised when 1 n \u00b5 = X = n i\u2211=1Xi , the pattern mean. (10 marks) (b) Calculate the cost of the pattern variance s 2(X) for the AQHI info in Desk Q2, giving your resolution moral to 2 decimal locations. (5 marks) Question 3 (a) Define a perform f : R \u2212\u2192 R by where a and b are precise constants. (i) Resolve the fluctuate of values of a and b such that f is staunch at x= (5 marks) (ii) The use of the restrict definition of differentiability, resolve the fluctuate 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 corner O actual reaches a degree P on the side AC as shown in Figure Q3b. Let OA = a and OB = b, where 0 < a < b, and let x = AP. As P strikes from A to C, the square of the dimensions of the crease fashioned by the fold is given by the perform L 2(x) : [0,b] \u2212\u2192 R outlined by \u00a0 (i) Resolve whether the perform L 2(x) is staunch over [0,b]. (5 marks) (ii) Resolve the fluctuate of values of a and b, enviornment to 0 < a < b < \u221e, such that the perform\u221a L 2(x) has a wander most over [0,b] at x = b\u2212\u00a0\u00a0\u00a0\u00a0\u00a0 b 2 \u2212a 2. (10 marks) Question 4 (a) Trace that the tangent line to the graph of the equation y 2 =x 3 on the point 8\/9, 16\u221a2\/27 is additionally a protracted-established to the graph in some unspecified time in the future. (5 marks) (b) Trace that the tangent lines to the graph of the equation y 2(x\u22121) = x 2(x+1) on the capabilities where x = 2 intersect at an perspective of . (3 marks) Question 5 END OF ASSIGNMENT\n<\/p>\n","protected":false},"excerpt":{"rendered":"
MTH109 Tutor-Marked Task 1 This assignment is fee 10% of the last sign for MTH109 Calculus. The closing date for this assignment is 05 March 2026, 2355hrs. Veil to Students: You are to incorporate the next particulars to your submission: Path Code, Title of the TMA, SUSS PI No., Your Title, and Submission Date. As […]<\/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-30026","post","type-post","status-publish","format-standard","hentry","category-solutions"],"_links":{"self":[{"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/posts\/30026","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=30026"}],"version-history":[{"count":0,"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/posts\/30026\/revisions"}],"wp:attachment":[{"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/media?parent=30026"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/categories?post=30026"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/academicwritersbay.com\/solutions\/wp-json\/wp\/v2\/tags?post=30026"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}