Having problems with a few of these, thanks for any help in advance.

This one is to be answered in terms of the constants involved

lim ((3/h)-(3/a))/(h-a)

h->a

lim (cos(x)-2)/(sin(x))

x->0

lim ((1/(h+3)^2)-(1/9))/h

h->0

Thanks Again

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- Jan 23rd 2008, 05:42 PMcasesamA few questions involving limits
Having problems with a few of these, thanks for any help in advance.

This one is to be answered in terms of the constants involved

lim ((3/h)-(3/a))/(h-a)

h->a

lim (cos(x)-2)/(sin(x))

x->0

lim ((1/(h+3)^2)-(1/9))/h

h->0

Thanks Again - Jan 23rd 2008, 08:13 PMmr fantastic
The first can be easily found by recognising it as being the derivative evaluated at x = a of the function f(x) = 1/x ......

For the second, the limit is -oo since you have a form -1/0.

For the third, you should recognise it as being the derivative evaluated at x = 3 of the function f(x) = 1/x^2 ...... - Jan 24th 2008, 02:27 AMtopsquark
In case you don't know derivatives yet I'll do the first one. The third one is worked out by a similar method.

$\displaystyle \lim_{h \to a} \frac{\frac{3}{h} - \frac{3}{a}}{h - a}$

Multiply numerator and denominator by ha to remove the complex fractions:

$\displaystyle \lim_{h \to a} \frac{3a - 3h}{ah(h - a)}$

Now do some factoring and you are done.

-Dan