Can someone show me the steps of calculating the limit of the following function?
When x approaches 1 from the left (1 minus), the limit of exp {(4-5x)/(1-x)}.
Thank you very much
Can someone show me the steps of calculating the limit of the following function?
When x approaches 1 from the left (1 minus), the limit of exp {(4-5x)/(1-x)}.
Thank you very much
Oh, yes... what I was concerning was that since it is 1 - x in the denominator, I cannot directly apply the limit to the fraction.
But thanks Archie! I know how to work it out now! What I need is to take the inverse, (1/x) / (4 - 5x) and evaluate the limit when x approaches 1 from the left and then take the inverse again. That is, the inverse of the limit of the inverse of a fraction is equivalent to the limit of the original function!
I am so happy today! Thanks for letting me know the existence of mathematica!
$\displaystyle \displaystyle\frac{4-5x}{1-x}$
The fraction is not defined for $\displaystyle x=1$ as this will cause the denominator to be zero.
$\displaystyle x=1$ does not cause a problem for the numerator, however.
As x approaches 1 from below, the fraction is negative, the denominator approaches zero and hence the fraction approaches $\displaystyle -\infty$
As x approaches 1 from above, the fraction is positive, the denominator approaches zero and hence the fraction approaches $\displaystyle +\infty$
$\displaystyle \displaystyle\lim_{y\rightarrow\infty}e^y$ doesnt exist since $\displaystyle e^y\rightarrow\infty$ as $\displaystyle y\rightarrow\infty$
$\displaystyle \displaystyle\lim_{y\rightarrow\ -\infty}e^y=0$