Find the limit (1-cos (x) ^ 2) ^ 0.5 / (1-cosx), where x approaches 0 The molecule is cos (x) ^ 2, not (cosx) ^ 2

Find the limit (1-cos (x) ^ 2) ^ 0.5 / (1-cosx), where x approaches 0 The molecule is cos (x) ^ 2, not (cosx) ^ 2

From the title,
lim(x→0) √[1-cos(x²)] / (1-cosx)
=lim(x→0) √[0.5x^4] / (0.5x²)
=lim(x→0) √[0.5]*x² / (0.5x²)
=√(0.5) / 0.5
=2√(1/2)
=√2
[because LIM (x → 0) [1-cosx] / [0.5 * X & # 178;] = 1]
[1-cosx and 0.5x & # 178 are equivalent infinitesimals, which can be replaced in the product factor]
[similarly, 1-cos (X & # 178;) and 0.5x ^ 4 are equivalent infinitesimals, which can also be replaced in the product factor]
[where √ is the root]
Hope to adopt~~~