Recent content by FaroukYasser

Homework Statement [/B] A 0.393 m long metal bar is pulled to the left by an applied force F. The bar rides on a parallel metal rails connected through a 42.9 ohm resistor as shown in the figure. So the apparatus makes a complete circuit. You can ignore the resistance of the bars and the rails...

I see. Thanks all!

Thanks. But I was hoping for a non linear function. Or in other words, I am wandering what this means geometrically. I know that if a point is an inflection point then its second derivative is 0 but the converse doesn't necessarily hold. In other words, what does f''(x_0) = 0 tell us about that...

I was wandering, can $$\ \frac { d^{ 2 }y }{ dx^{ 2 } } | _{ x={ x }_{ 0 } }=\quad 0$$ if $$\frac { dy }{ dx }| _{ x={ x }_{ 0 } }\neq \quad 0$$ and if so, what does this translate to geometrically?

Wolfram exceeded time on the original expression without breaking it down. (Although I have no idea why it did) And thanks for answering :)

Homework Statement For $$\lim _{ x\rightarrow \infty }{ \frac { { x }^{ 2 }+{ e }^{ -{ x }^{ 2 }\sin ^{ 2 }{ x } } }{ \sqrt { { x }^{ 4 }+1 } } } $$, determine whether it exists. If it does, find its value. if it doesn't, explain. Homework Equations Sand witch theorem and arithmetic rule...

Homework Statement Prove that if a bound sequence ##\left\{ { X }_{ a } \right\} ## is divergent then there are two sub sequences that converge to different limits. Homework Equations None. The Attempt at a Solution Ok so I am not sure if my attempt for a solution is correct or not, but I...

Thanks a lot!

Thanks. I was wandering though, is my method ok or does it have any flaw in the logic? I am just trying to exercise with the sandwich theorem so I just want to make sure the steps are moving logically. And dividing the numerator and denominator by n^(2/3) would do the trick right?

Hint: Try multiplying the expression by: ##\frac { \sqrt { z + i } }{ \sqrt { z + i } } ## Moderator note: I revised the expression above to convey what FaroukYasser meant, but did not write.

Homework Statement Show that ##\lim _{ n\rightarrow \infty }{ \left( \frac { \sqrt { n+c } +d }{ \sqrt [ 3 ]{ { n }^{ 2 }+an+b } } \right) } =0,\quad n>-c ## Homework Equations Sandwich theorem The Attempt at a Solution Ok, So I know my method is extremely long, I'm just wandering if 1)...

1 Thanks a lot for your help, and sorry if I bothered you with my not so intelligent questions :)

Aha, I see. Also, would the way I used with lots of algebra be considered a correct proof or faulty?

Well if both tend towards 0 then using the arithmetic rule, then the sum of them tends towards 0. Do you mean that I should divide it to two such as root(n+3) - root(n+1) once and show it tends towards 0 then use do root(n+3) - root(n+2) and show that this also tends towards 0 and using the...

##Using\quad your\quad hint:\\ \left| \sqrt { n+1 } -\sqrt { n+3 } \right| =\sqrt { n+3 } -\sqrt { n+1 } =\quad \frac { n+3-n-1 }{ \sqrt { n+1 } +\sqrt { n+3 } } <\frac { 2 }{ \sqrt { n+1 } +\sqrt { n+3 } } <\frac { 2 }{ \sqrt { n } } ,\quad therefore\quad take\quad N=\left( \frac { 2 }{ \E...