math_limit_doubt_questions FindlimitusingL'HospitalRule1.limx-๐›ผsinx-sin๐›ผx-๐›ผ=limx-๐›ผcosx1=cos๐›ผ FindlimitusingL'HospitalRule2.limx-0(1+x)n-1x=limx-0(n)(1+x)n-11=(n)(1)n-1=n FindlimitusingL'HospitalRule3.limx-0(1-x)-13(1-x)-23=limx-0(-13)(1-x)-13-1(-23)(1-x)-23-1=-13-23=12 FindlimitusingL'HospitalRule4.limx-0(ex2-cosx)x2=limx-0(2x)ex2+sinx2x=limx-0(2x)(2x)ex2+(x)(2x)ex2+cosx2=cos02=12 FindlimitusingL'HospitalRule5.limx-0(x-tan-1x)x-sinx=limx-01-11+x21-cosx=limx-0(2x)(1+x2)-2sinx=limx-0[2][(1+x2)-2-4x2(1+x2)-3]cosx=2 FindlimitusingL'HospitalRule5.limx-0xcosx-sinxx2sinx=limx-0-xsinx+cosx-cosxx2cosx+2xsinx=limx-0-xsinxx2cosx+2xsinx=limx-0-xcosx-sinx-x2sinx+2xcosx+2xcosx+2sinx=limx-0-xcosx-sinx-x2sinx+4xcosx+2sinx=limx-0xsinx-cosx-cosx-x2cosx-2xsinx-4xsinx+4cosx+2cosx=-26=-13