various calculus problems for review

[Vader07]

Hey guys,

I have couple of issues with the following 6 problems:

1).
lim x^3 (sin^2) ( 1/x) =?
x > 0

the > is the sign for an arrow pointing to zero. I don't know how to solve for sin version of limits. I got the answer of 0 but it doesnt seem right (just simple plug in?)

2.) Suppose you know that h is an odd function,
and that lim h(x) = -5. Then lim h(x) = ?
x > 3^+ x > -3^-

3.) for y = (x-2)/(x-3) i wanted to know is this removable or non-removable

i thought it would be non-removable discontinuity but my friend says im wrong

4.) g(x) = 2/3x, [x, x + h],

this is dealing with derivatives
i got 2 / 3 (x + h) x for my answer

5.) Find d / dx at the point (0, p/2) on the curve implicitly defined by
cos [Pi(x^3)-y] = xy

I got Pi (3.14) as my final answer

6.) Find dy/dx at the point (1, 1) on the curve implicitly defined by
(x^3)(y) -3(x^2) + 4(y^3) = 2

Any help or tips would be greatly appreciated. Thanks in advance

 

[tkhunny]

(just simple plug in?)

Never, ever do that. If this is your plan, you are not getting it. Read the section again.

 

[tkhunny]

but it doesnt seem right

This is mathematics. Is it right or isn't it? Did you follow an appropriate trail or not? Guessing just is not very reliable.

 

[tkhunny]

1).
lim x^3 (sin^2) ( 1/x) =?
x > 0

I suspect that you should leverage the result from a similar limit using [sin(x) / x]. It might just work for [sin(1/x) / (1/x)] with a little modification.

 

[tkhunny]

2.) Suppose you know that h is an odd function,
and that lim h(x) = -5. Then lim h(x) = ?
x > 3^+ x > -3^-

Please state the definition of a Odd Function. Apply this defintiion to the function in the limit.

3.) for y = (x-2)/(x-3) i wanted to know is this removable or non-removable

i thought it would be non-removable discontinuity but my friend says im wrong

Exactly what theorem are you quoting when you say "my friend says I'm wrong"? Remember, this is mathematics. Prove it, don't rumor it.

There is an unavoidable asymptote at x = 3. How is that removable?

Did your "friend" invite you to a "safe" party, too? Don't go.

4.) g(x) = 2/3x, [x, x + h],

this is dealing with derivatives
i got 2 / 3 (x + h) x for my answer

I can't understand this one. Please quote the ENTIRE problem statement and show your methodology.

5.) Find d / dx at the point (0, p/2) on the curve implicitly defined by
cos [Pi(x^3)-y] = xy

I got Pi (3.14) as my final answer

Great. Too bad no one can tell you if you followed a proper path. Please show your work. What did you get for dy/dx?

6.) Find dy/dx at the point (1, 1) on the curve implicitly defined by
(x^3)(y) -3(x^2) + 4(y^3) = 2

Same response as the previous question. Show your work.