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**fusilli_jerry89****Member**- Registered: 2006-06-23
- Posts: 86

lim (2- √(6-x))/(x-2)

x->2

lim (3x²-x+1)/(x+3)

x->-3-

lim (√(x+Δx)- √(x))/Δx

Δx->0

lim (sin3x)/x

x->0

lim (x+2)/(x³+8)

x->-2

Without graphing

*Last edited by fusilli_jerry89 (2006-10-22 18:38:31)*

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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 118

1)

(for all x not equal to 2)Hence:

*Last edited by gnitsuk (2006-10-22 21:43:42)*

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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 118

3)

for all dx not equal to zero.Hence:

*Last edited by gnitsuk (2006-10-22 21:43:54)*

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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 118

4)

For this we need to make use of the important result:

Let

then*Last edited by gnitsuk (2006-10-22 22:03:52)*

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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 118

5)

for all x not equal to -2.Hence:

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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 118

2)

Here the limit is not finite. As x approaches -3 from -'ve infinity the given function approaches -infinity

so:

*Last edited by gnitsuk (2006-10-22 23:00:15)*

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

L'Hopital's rule would be very useful in some of those.

It states that if f(x) and g(x) are both undefined for some value of x (call it p), then:

.Why did the vector cross the road?

It wanted to be normal.

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**fusilli_jerry89****Member**- Registered: 2006-06-23
- Posts: 86

gnitsuk wrote:

2)

Here the limit is not finite. As x approaches -3 from -'ve infinity the given function approaches -infinity

so:

when I graph it, it looks like as it approaches -3 from the negative side, it rises to positive infinite, not negative.

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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 118

Here you can see that as x tends to -3 from -infinity the value of the function is heading to -infinity.

You might have entered the function incorrectly?

Mitch.

*Last edited by gnitsuk (2006-10-25 21:54:52)*

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**fusilli_jerry89****Member**- Registered: 2006-06-23
- Posts: 86

oh woops, my window setting were too small, i didnt see the other part of the function.

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