1. ## Limits help

1. Find the lim x goes to 4 on the postive side of the function x-5/(4-x^3)(x-7)^2.
2. Find the lim x goes to postive Pi/2 of the function tan x.
3. Find the lim x goes to infinity (2x+1)/x^2-(2x-1)/x^2.
4. Find the lim x goes to infinity (x^2)/(2x+1) - (x^2)/(2x-1)
5. Fiind the lim x goes to infinity x^3/3^x

2. Originally Posted by Nimmy
1. Find the lim x goes to 4 on the postive side of the function x-5/(4-x^3)(x-7)^2.[/tex]
It is countinous, simplfy substitute 4 for x
2. Find the lim x goes to postive Pi/2 of the function tan x.
The limits does not exist, however $\displaystyle +\infty$

5. Fiind the lim x goes to infinity x^3/3^x
Exponential always overtake polynomials so the limit is zero.

3. Originally Posted by Nimmy
4. Find the lim x goes to infinity (x^2)/(2x+1) - (x^2)/(2x-1)

$\displaystyle \frac{x^2}{2x+1} - \frac{x^2}{2x-1}=\frac{x^2(2x-1)-x^2(2x+1))}{4x^2-1}=-\frac{2x}{4x^2-1}$$\displaystyle =\frac{2}{4+1/x^2} Therefore: \displaystyle \lim_{x \to \infty} \frac{x^2}{2x+1} - \frac{x^2}{2x-1}=$$\displaystyle \lim_{x \to \infty}\frac{2}{4+1/x^2}=1/2$

RonL

4. ## Math Help Homework

Find the lim x goes to inifinity (2/3x-4)? and also for the equation of square root of 4x+1.

5. Is the first one $\displaystyle \lim_{x \rightarrow \infty} \frac{2}{3}x-4$ or $\displaystyle \lim_{x \rightarrow \infty}\frac{2}{3x}-4$?

6. Ok nvr mind about that problem but i do need help on square root of 4x+1 using the def. of dervitaitve. Dont use the calculus way!!!

7. Originally Posted by Nimmy
Ok nvr mind about that problem but i do need help on square root of 4x+1 using the def. of dervitaitve. Dont use the calculus way!!!
How can we not use Calculus if we are using the definition of a derivative??

-Dan

For the record:
$\displaystyle \frac{d}{dx}\sqrt{4x+1} = \frac{2}{\sqrt{4x+1}}$ which is positive for all x in its domain, so we see that $\displaystyle \sqrt{4x+1}$ is monotonically increasing on $\displaystyle [ -\frac{1}{4}, \infty )$ and it has no horizontal asymptote. Thus $\displaystyle \lim_{x \to \infty} \sqrt{4x+1} \to \infty$.

8. Originally Posted by Nimmy
Find the lim x goes to inifinity (2/3x-4)? and also for the equation of square root of 4x+1.
What about $\displaystyle \sqrt{4x+1}$ is it that you want help with?

RonL

9. ## Math Help Homework

Find a and b so that the slope of the tangent line to f(x)= ax^2+bx (1,3) is -2.

10. Originally Posted by Nimmy
Find a and b so that the slope of the tangent line to f(x)= ax^2+bx (1,3) is -2.
When you are asking a new question, please start a new thread. It's much less confusing that way, and much easier for someone else to find help on a similar problem.

The slope of the tangent line to $\displaystyle f(x) = ax^2 + bx$ is the first derivative $\displaystyle f'(x) = 2ax + b$. At the point (1,3) $\displaystyle f'(1) = 2a + b = -2$. There are many possible solutions to this equation, so I'll simply say that you can pick any "a" value and the required "b" value will then be $\displaystyle b = -2a - 2$.

-Dan

11. So do u basically plug in -2a-2 into f'(x) or f(x)?