# A few questions involving limits

• Jan 23rd 2008, 05:42 PM
casesam
A 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 PM
mr fantastic
Quote:

Originally Posted by casesam
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

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 AM
topsquark
Quote:

Originally Posted by casesam
lim ((3/h)-(3/a))/(h-a)
h->a

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