SOLUTION: Please give steps on how to solve these two limit problem, pretty new to these.
lin x ->0 Ln(sin|x|)
lim x -> - ∞ (3+t)/(sqrt(1+9t^2))
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-> SOLUTION: Please give steps on how to solve these two limit problem, pretty new to these.
lin x ->0 Ln(sin|x|)
lim x -> - ∞ (3+t)/(sqrt(1+9t^2))
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Question 983090: Please give steps on how to solve these two limit problem, pretty new to these.
lin x ->0 Ln(sin|x|)
lim x -> - ∞ (3+t)/(sqrt(1+9t^2)) Answer by jim_thompson5910(35256) (Show Source):
As x approaches 0, the quantity |x| approaches 0. Have a look at the graph of y = |x| if you aren't sure. Or look at a table of function values.
Specifically, |x| is approaching 0 from the right. It is never negative which means it can never approach 0 from the left.
So sin(|x|) approaches sin(0) which approaches 0 itself. Because sin(x) is positive for small values of x such that x > 0, this means that sin(|x|) is approaching 0 from the right.
So far, we know that if x gets closer and closer to 0, then sin(|x|) gets closer and closer to 0 from the right.
Therefore, Ln(sin(|x|)) becomes Ln(y) where y approaches 0 from the right. Ln(y) is undefined when y = 0, but we can plug in very very small values of y to find that Ln(y) is approaching negative infinity. A table or graph will show this.
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