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Determine the infinite limit.

$ \displaystyle \lim_{x \to 0^+}\ln (\sin x) $

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 2

The Limit of a Function

Limits

Derivatives

Harvey Mudd College

Baylor University

Idaho State University

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This is problem number thirty six of Stuart eighth Edition, section two point two Determine the infinite limit the limit as experts zero from the right of the function Helen Quantity Sign of X. We'LL begin I estimating a number of very close A zero something very small but positive. And see how that might look here in our function if we plugged it him. How about using this notation? Zero the superscript positive Did you know a number that's very, very close to zero but very, very small such as zero point zero zero zero one, for example the sine function as he approached hero from the right four Just in general, the sine function of zero Can't you number that is very close to zero and also very small and positive. So the solution will be dependent on what the block arithmetic function looks like. Very close to zero in a plant full arrhythmic function the natural log and six approaches zero from the right we see that the natural long tends towards negative infinity. And so, with the decent amount of certainty, we can confirm the limit here ten stories negative infinity. We will use a graph of this function Enter observed the behaviour as experts zero from the right to confirm our solution. This is a plant of Helen of sign of X and as we see as a function of purchase hero from the right, devalues get increasingly more negative which confirms our solution that the limit of Ellen of it sign of X and sex purchase here from the rate is negative infinity.

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