Search for: If f(x)=limn→∞ ∑r=0n tanx2r+1+tan3x2r+11−tan2x2r+1 then limx→0 f(x)x is equal toIf f(x)=limn→∞ ∑r=0n tanx2r+1+tan3x2r+11−tan2x2r+1 then limx→0 f(x)x is equal toA1B0C-1DNone of these Register to Get Free Mock Test and Study Material +91 Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:Let αr=x2r+1,r=0,1,2,…,n. Then, tanx2r+1+tan3x2r+11−tan2x2r+1=tanα+tan3αr1−tan2αr=tanαr1+tan2αr1−tan2αr =tanαrcos2αr=sinαrcosαrcos2αr=sin2αr−αrcosαrcos2αr=tan2αr−tanαr∴ f(x)=limn→∞ ∑r=0n tan2αr−tanαr⇒ f(x)=limn→∞ ∑r=0n tanx2r−tanx2r+1⇒ f(x)=limn→∞ tanx−tanx2n+1=tanxHence, limx→0 f(x)x=limx→0 tanxx=1Post navigationPrevious: The value of limx→0 sinx−x+x36x5 isNext: If limx→∞ x2+1x+1−ax−b=2, then Related content JEE Main 2023 Question Papers with Solutions JEE Main 2024 Syllabus Best Books for JEE Main 2024 JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria JEE 2024: Exam Date, Syllabus, Eligibility Criteria NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3 JEE Crash Course – JEE Crash Course 2023 NEET Crash Course – NEET Crash Course 2023 JEE Advanced Crash Course – JEE Advanced Crash Course 2023