The limit of the function e^(1/(6-x)) as x approaches 6 from the right is definitively 0. This conclusion is reached by analyzing the behavior of the term 1/(6-x), which approaches negative infinity as x approaches 6 from the right. Consequently, e raised to a negative infinity results in 0. Any reference to the limit being e^(17/3) is incorrect, confirming that the book's answer is erroneous.
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Hello tsaitea. Welcome to PF !tsaitea said:lim e^(1/(6-x))
x->6+
Was wondering how to solve for this limit analytically. I plotted it and see it going to 0, but that is not the answer in the book.
Actually \displaystyle \ \ \lim_{x\to6^{+}}\,\frac{1}{6-x}=-\infty\ .tsaitea said:oh -infinity, but the answer is e^(17/3)?, maybe the book is wrong then?