Question

HELP!!!!
let f(x) = sqrt of -1-x if x<2
1 if x = -2
3x+8 if x>2


Calculate the limits:
lim x of -2- f(x)=?
lim x of -2+ f(x)=?
lim x of -2 f(x)=?

Answer 1

plug in -2 and see what you get

Answer 2

i am assuming you meant
\[f(x) = \left\{\begin{array}{rcc}
\sqrt{-1-x} & \text{if} & x <-2 \\
1& \text{if} & x=-2 \\
3x+8 & \text{if} &x>-2
\end{array}
\right.\]

Answer 3

otherwise question doesn't really make sense

Answer 4

showing off your piecewise function skills again I see :)

Answer 5

lovingly stolen from zarkon (tm)

Answer 6

actually i only stole the text part i had the rest from google

Answer 7

thats correct except the top should be square root of -1-x +1

Answer 8

like this?
\[f(x) = \left\{\begin{array}{rcc}
\sqrt{-1-x} +1& \text{if} & x <-2 \\
1& \text{if} & x=-2 \\
3x+8 & \text{if} &x>-2
\end{array}
\right.\]

Answer 9

yes

Answer 10

in this case if you plug in -2 in the first formula you get 2

Answer 11

and if you plug in -2 in the last formula you also get 2

Answer 12

so the limit from the left is 2, the limit from the right is 2, and since they agree, that limit is 2

Answer 13

ok so for these you just plug in for x?

Answer 14

what the actual values is at x = -2 is irrelevant as far as the limit is concerned

Answer 15

so that answer would be does not exist?

Answer 16

yes don't make it as hard as your calc teacher makes it seem

Answer 17

oh no that answer is the limit is 2

Answer 18

let me write it out

Answer 19

\[\lim_{x\rightarrow -2^-}=\sqrt{-1-(-2)}+1=2\] and
\[\lim_{x\rightarrow -2^+}=3\times (-2)=8=2\] and since
\[\lim_{x\rightarrow -2^-}f(x)=\lim_{x\rightarrow -2^+}f(x)=2\] then
\[\lim_{x\rightarrow -2}f(x)=2\]

Answer 20

typo line 3 should have been \[\lim_{x\rightarrow -2^+}=3\times (-2)+8=2\]

Answer 21

ok thanx! what about this one: find in terms of the constant a.
lim h of 0 5(a+h)squared - (5a)squared
____________________________
h

Answer 22

is that \
\[\lim_{h \rightarrow 0}\frac{5(a+h)^2-5a^2}{h}\]?

Answer 23

yes

Answer 24

two ther people on here gave me answers that were wrong. so im hoping you can help

Answer 25

sure

Answer 26

my answers have been wrong also. im supposed to find in terms of the constant a.

Answer 27

lets go slow.
\[(a+h)^2=a^2+2ah+h^2\]

Answer 28

right

Answer 29

\[5(a+h)^2=5a^2+10ah+5h^2\]

Answer 30

and so
\[5(a+h)^2-5a^2=10ah+5h^2\]

Answer 31

divide by h to get
\[\frac{10ah+5h^2}{h}=\frac{h(10a+5h)}{h}=10a+5h\]

Answer 32

now take the limit as h goes to zero get
\[\lim_{h \rightarrow 0}\frac{5(a+h)^2-5a^2}{h}=\lim_{h \rightarrow 0}10a+5h=10a+5\times 0=10a\]

Answer 33

YES! THANX!

Answer 34

yw
and don't fret, in a week you will do this in your head in 1 second

Answer 35

you will say to yourself
"the derivative of
\[x^2\] is
\[2x\] so the derivative of
\[5x^2\] is
\[10x\] finished

Answer 36

AWESOME! I got some other questions Ill get back on later and see if we came up with the same answers!