Search for: The values of a and b such that limx→0 x(1+acosx)−bsinxx3=1, are The values of a and b such that limx→0 x(1+acosx)−bsinxx3=1, are A52,32B52,−32C−52,−32Dnone of these Fill Out the Form for Expert Academic Guidance!l Grade ---Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12 Target Exam JEENEETCBSE +91 Preferred time slot for the call ---9 am10 am11 am12 pm1 pm2 pm3 pm4 pm5 pm6 pm7 pm8pm9 pm10pm Please indicate your interest Live ClassesBooksTest SeriesSelf Learning Language ---EnglishHindiMarathiTamilTeluguMalayalam Are you a Sri Chaitanya student? NoYes Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:We have, limx→0 x(1+a cosx)−b sinxx3=1⇒limx→0 x1+a1−x22!+x44!−x66!+…−bx−x33!+x55!…x3=1⇒limx→0 (1+a−b)+x2b3!−a2!+x4a4!−b5!+…x2=1 … (i) If 1+a−b≠0, then LHS →∞ as x→0 while RHS =1∴ 1+a−b=0From (i), we havelimx→0 x2b3!−a2!+x4a4!−b5!+…x2=1∴ b3!−a2!=1⇒b−3a=6Solving 1 + a - b = 0 and b - 3 a = 6, we get a=−52,b=−32 Related content Nucleus Diagram for Class 9 Neuron Diagram Class 9 Human Heart Diagram Class 10 CBSE Class 7 Science Chapter 1 Nutrition in Plants MCQ Questions with Answers CBSE Class 9 English Worksheet – The Road not Taken 50+ GK Questions and Answers for Class 8 “Kabir Ki Sakhiyan” MCQ Questions for Class 9 Hindi with Answers Kshitij, Kritika, Sparsh, Sanchayan Bhag 1 CBSE Class 7 English Honeycomb Chapter 1 Three Questions MCQ Questions with Answers CBSE Class 9 English Beehive Book Poem 1 The Road Not Taken MCQ Questions with Answers MCQs Questions with Answers for Class 9 English Chapter 1 The Fun They Had