Why that cosx got disappeared ! Kindly explain - Maths - Continuity and Differentiability

Question

Why that cosx got disappeared ?! Kindly explain

Lovina Kansal · Accepted Answer

Dear student
We have,limx→0sin5x3x+cosx=f(0)⇒limx→0sin5x3x+limx→0cosx=f(0)⇒limx→0sin5x3x+1=f(0)  ∵limx→0cosx=cos(0)=1⇒limx→05sin5x5×3x+1=f(0)⇒53limx→0sin5x5x+1=f(0)⇒53+1=f(0)⇒f(0)=83=k
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Why that cosx got disappeared ?!.. Kindly explain.