Aug 6th, 2022

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heres a question for you how would you evaluate this limit what is the limit as n goes to infinity of a 1 plus 1 over n raised to the n power well in this video were going to talk about how to evaluate this limit so the first thing were going to do is were going to set the entire expression equal to y so our goal is to solve for y if we can do that we could find the value of this expression now the next thing that were going to do is were going to take the natural log of both sides so were going to have ln y is equal to the limit as n goes to infinity and then the natural log of 1 plus 1 over n raised to the n now a property of logs lets say we have log x raised to the a we can take the exponent and move it to the front so ln x raised to the a power is a times ln x so were going to take this variable move it to the front so were going to have the natural log of y is equal to the limit as n goes to infinity n times the natural log of one plus one over n now we still have some

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Formula. The limit of the quotient of natural logarithm of one plus a variable by the variable as the input approaches zero is equal to one. It is called the natural logarithmic limit rule.

1:14 4:08 using logarithms to solve limits - YouTube YouTube Start of suggested clip End of suggested clip The logarithm of a limit is equal to the limit of the logarithm.MoreThe logarithm of a limit is equal to the limit of the logarithm.

0:53 5:17 Limits of Logarithmic Functions | Calculus - YouTube YouTube Start of suggested clip End of suggested clip This is equal to the limit. As x approaches a of f prime of x divided by g prime of x. So if we wereMoreThis is equal to the limit. As x approaches a of f prime of x divided by g prime of x. So if we were to take the derivative of the top and the bottom.

The argument of a log function can only take positive arguments. In other words, the only numbers you can plug into a log function are positive numbers. Negative numbers, and the number 0, arent acceptable arguments to plug into a logarithm, but why?

Because ln is a continuous function it preserves limits.

0:53 5:17 Limits of Logarithmic Functions | Calculus - YouTube YouTube Start of suggested clip End of suggested clip And heres the gist of lhopitals rule lets say if we want to evaluate the limit as x approaches aMoreAnd heres the gist of lhopitals rule lets say if we want to evaluate the limit as x approaches a of f of x over g of x. This is equal to the limit.

The limit of a function is a branch of calculus that deals with the derivative of the function. It is the rate of change of function as the points in the domain change. Logarithmic functions are inverse exponential functions whose limit can be calculated using the methods discussed in this section.

The limit of ratio of logarithm of to a base to is equal to reciprocal of natural logarithm of base.

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