+84 Find by direct substitution
lim x-8
x --> y ------------------
x^2 + 13x + 42
a. limit does not exist
b. -1/240
c. 1/240
d. 0
e. infinity
Find
lim 'squareroot' 14+y - 'squareroot' 14
y --> 0 -----------------------------------------------
y
a. 'squareroot' 14 / 2
b. 'squareroot' 14 / 28
c. limit does not exist
d. 0
e. 'squareroot' 14 / 14
+118690 Find by direct substitution
lim x-8
x --> y ------------------
x^2 + 13x + 42
a. limit does not exist
b. -1/240
c. 1/240
d. 0
e. infinity
Are you sure you want x tends to y ??
If you do then just replace the x's with y's
Find
lim 'squareroot' 14+y - 'squareroot' 14
y --> 0 -----------------------------------------------
y
I am using L'Hopital's rule to sove this:
If you do not know the rule you should watch this clip.
\(\displaystyle\lim_{y\rightarrow0}\; \frac{\sqrt{14+y}+\sqrt{14}}{y}\\ =\displaystyle\lim_{y\rightarrow0}\; \frac{(14+y)^{1/2}+\sqrt{14}}{y}\\ \mbox{I am going to differentiate top and bottom separately with respect to y }\\ =\displaystyle\lim_{y\rightarrow0}\; \frac{(1/2)(14+y)^{-1/2}}{1}\\ =\displaystyle\lim_{y\rightarrow0}\; \frac{1}{2\sqrt{14+y}}\\ =\frac{1}{2\sqrt{14+0}}\\ =\frac{\sqrt{14}}{28}\\ \)
