I need help in this Limit: lim_[x -> 0] [(sin(pi) sqrt(cos(x))] / [x]

Ilyasde

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Can someone help me please in this Limit, I have the exam soon ? ? Tyy
 

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Hello. Did you begin by substituting a value for the sine of pi? Please share your work thus far. Thank you!

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Hello. Did you begin by substituting a value for the sine of pi? Please share your work thus far. Thank you!

[imath]\;[/imath]
No. It's sin(pi) from the question.
 
To evaluate the limit:

lim_[x → 0] [(sin(π) sqrt(cos(x))] / [x]

We can use the fact that sin(π) = 0 and cos(0) = 1 to simplify the expression as follows:

lim_[x → 0] [(sin(π) sqrt(cos(x))] / [x]

= lim_[x → 0] [(0) sqrt(cos(x))] / [x] (substituting sin(π) = 0)

= lim_[x → 0] 0 / [x]

= 0

Therefore, the limit is equal to 0.
 
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