I need help in this Limit: lim_[x -> 0] [(sin(pi) sqrt(cos(x))] / [x]
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mmm4444bot
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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]
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topsquark
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Did you copy the problem correctly? Is there supposed to be an x inside the sine function?
-Dan
No. It's sin(pi) from the question.
BigBeachBanana
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Well, you didn't answer @mmm4444bot's question: What's the value of [imath]\sin(\pi)?[/imath]
The answer is quite obvious once you've done that.
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.
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.