Recent content by ManicPIxie

OOOOOKKKKK. So, ln[(x-10)(x-3)/(x-d)] has to be defined for the limit to exist. We want to chose a value of d such that the denominator cancels part of the numerator. If d=-3, then we have lim x-> -3 ln(x-10) = ln(-13), which is undefined. So try d=10 lim x->10 ln(x-3) =ln(7) which is...

Okay, so d must be limited to a small number because we don't want it to go to infinity (otherwise we wouldn't be able to find the value for d). Also, d must be positive because a negative log isn't defined and we don't have a value for d in the numerator to make the overall quotient positive...

Okay, I can't answer that with my current knowledge. Before I go on, would you happen to be aware of some reading that would explain this situation to me?

Okay, so a logarithm function is only defined for real, positive vales of x. In addition, while one sided limits do exist, the log function is a continuous function so if the LH limit exist, the RH limit exists, and in the case, the limits must be equal.

Homework Statement For which value of d does the following limit exist? lim x->d ln [ (x2-13x+30) / (x-d) ] Homework Equations None The Attempt at a Solution I understand how to find limits when the limit goes to a real number, and has a variable in the function to solve for, but not when...

This question comes from a previous years exam as practice for my upcoming. Homework Statement Two spaceships are launched from Earth, going in opposite directions. Eventually, both spaceships have a velocity of 0.75c (where c is the speed of light), each in their respective directions. A...

Aha! And entering that into Maple TA works! Thanks for your help!

:/ Okay, my bad. Retry: [(x^6 - 10)/(x^3 + 1)] ⋅ 3x^2 = (3x^8 - 30x^2)/(x^3 + 1)

In the cancelling step: [(3x^6 - 10)/(x^3 + 1)] ⋅ 3x^2 It canceled to give: (x^3 - 10) ⋅ 3x^2

Homework Statement F(x) = (integral from 1 to x^3) (t^2 - 10)/(t + 1) dt Evaluate F'(x) Homework Equations Using the chain rule The Attempt at a Solution Let u = x^3 Then: [((x^3)^2 - 10) / (x^3 + 1)] ⋅ 3x^2 *step cancelling powers of x from fraction* = (x^3 - 10)(3x^2) = 3x^5 - 30x^2 I am...

Thanks. I already drew a free body diagram, probably should have mentioned that. The two forces are the buoyant force provided by the fresh water, and the gravitational force. Where I'm stuck I suppose is mostly we aren't given the original weight of the ship, or does this not matter and I...

Homework Statement The Plimsoll line is a line marked on the side all ships that effectively indicates the safe maximum load the ship can carry in that type of water at that temperature.You have been asked to stand on the dock and collect the tickets of the passengers boarding a cruise ship...

Quite right Perok! Redoing my work after your find I have reached the following conclusion that checks out when plugged into vf = vi + at t1 = 200s t2 = 40s 40s also happens to be one fifth of 200s, making it such a lovely fit. Thank you all so much for your help.

Hello Aleph and Delta, thanks for your replies, sorry I didn't get back sooner, I was grinding away at this question and I think I have it but would like to let you two say what you think before I go ahead and submit it. Known: a1 = 0.100ms-2 a2 = 0.500ms-2 dtotal = 2.5km = 2500m vi = vf =...

Homework Statement There are two train stations, 2.5km (2500m) apart, therefore an ordinary suburban train cannot reach its max v between the two station. They try to minimise time taken by accelerating at a constant rate of 0.1ms-2 for time t1 and decelerate at 0.5ms-2 for time t2. Find the...