Question

How to prove
Lim (1-cosx)/x=0
x➡0

Answer 1

Explanation:

1−cosx=2sin2(x2) so

1−cosxx=(x4)⎛⎜ ⎜⎝sin(x2)x2⎞⎟ ⎟⎠2 then

limx→01−cosxx≡limx→0(x4)⎛⎜ ⎜⎝sin(x2)x2⎞⎟ ⎟⎠2=0⋅1=0

Answer 2

Answer:

Step-by-step explanation:

If we apply limit directly then we get indeterminate form

So differentiate numerator as well as denominator

lim(x->0) (0+sinx)/1

lim(x->0) sinx

apply limt now

sin0=0=rhs