Question

One sided limits! pls help me check if my answers are correct! :D

Answer 1

a.) 0
b.) 15
c.) 0
d.) 15
e.) 15
f.) 15

Answer 2

you sure about b) 15?

Answer 3

and d) and f)

Answer 4

\[\lim_{x \rightarrow 1}\frac{ x^2-1 }{ x-1 }=\frac{ 2x }{ 1 }=2\]
\[\lim_{x \rightarrow 3}\frac{ x^2-2x-3 }{ x-3 }=\frac{ 2x-2 }{ 1 }=4\]
\[\lim_{x \rightarrow b}\frac{ (x-b)^{50}-x+b }{ x-b }=50(x-b)^{49}\times -1= -1\]
\[\lim_{h \rightarrow 0}\frac{ \frac{ 1 }{ 5+h }-\frac{ 1 }{ 5 } }{ h }= \ln(5+h)=\ln5\]

can help me check about these too?

Answer 5

oh okay, i didn't see the minus, b.) 0, also d.) 0, i dont see whats wrong with f?

Answer 6

if x-> 5- and x->5+ are different, then x->5 will not exist!

Answer 7

oh i forgot about that, :p thanks! , btw the rest i used l'hopital's rule are my answers correct?

Answer 8

except the last one, all are correct

Answer 9

derivative of 1/(5+h) is not ln (5+h)!
did you do integration instead :P

Answer 10

it shd be \[\frac{ -1 }{ (5+h)^2 }\] i messed up haha then the answer wd be -1/25?

Answer 11

\[\lim_{x \rightarrow a}\frac{ x-a }{ \sqrt{x}-\sqrt{a}}, a>0\] one last qn, how do i approach this type of question?

Answer 12

yes, that was -1/25

numerator = x-a
treat it as
\(\large (\sqrt x)^2 -(\sqrt a)^2\)

Answer 13

apply formula a^2-b^2 = (a+b)(a-b)

Answer 14

need more help on this?

Answer 15

it'll look like this?
\[\lim_{x \rightarrow a}\frac{ (\sqrt{x}+\sqrt{a})(\sqrt{x}-\sqrt{a})}{ \sqrt{x}-\sqrt{a} }\]
then cancel left with
\[\lim_{x \rightarrow a}\sqrt{x}+\sqrt{a}\] \[= 2\sqrt{a}\]?

Answer 16

absolutely correct! :)

Answer 17

thank you! i appreciate your help! :D

Answer 18

welcome ^_^