Thread: A few questions involving limits

1. 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

2. 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 ......

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

Multiply numerator and denominator by ha to remove the complex fractions:
$\lim_{h \to a} \frac{3a - 3h}{ah(h - a)}$

Now do some factoring and you are done.

-Dan