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))
Algebra.Com
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): You can put this solution on YOUR website!
I'll do the first one to get you started.
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.
-------------------------------------------------------
In the end,
) = -\infty)
RELATED QUESTIONS
Please give steps on how to solve these two limit problem, pretty new to these.
lin x (answered by swincher4391)
1. let f(x) = ((2x-1)^2)/(2x^2)
find:
a. lim x->∞
b. lim x->-∞
c. lim (answered by Fombitz)
For each of the limits determine whether the limit exists as a number, as an infinite... (answered by Boreal)
Is this the right approach to solving limits?
ex:
lim x->∞ (ln(e^x-e^-x))/(x)
(answered by ikleyn,Alan3354)
What is each piece of information telling about the function exactly?
The function has (answered by jim_thompson5910)
Please explain how to solve this limit problem
lim ->0 (e^x-1)/x
I know my teacher (answered by solver91311)
How to solve this limit?
{{{lim(x->0, (cos(2x) - cos(x))/(0))}}}
Please explain... (answered by jim_thompson5910)
Evaluate the limit
lim x->-7 x=?
Please explain how to solve this... (answered by farohw)
Solve: ln x +ln (x+5)=ln(x^3 + 15x)-ln x
Not sure how to do this problem! please show... (answered by ankor@dixie-net.com)