Recent content by Joe20

I would like to know how can we determine or tell from the diagram that the electron domain is tetrahedral and molecular geometry is bent/ v-shaped? thanks

Note: $P_n (x)$ is legendre polynomial $$P_{n+1}(x) = (2n+1)P_n(x) + P'_{n-1}(x) $$ $$\implies P_{n+1}(x) = (2n+1)P_n(x) + \sum_{k=0}^{\lfloor\frac{n}{2}\rfloor} (2(n-1-2k)+1)P_{n-1-2k}(x))$$ How can I continue to use induction to prove this? Help appreciated.

Hi, I have solved this ODE till half way and got stucked on the integration of some weird expression. Need help for this. Thank you!

Hi, I have attached part of my steps for solving the homogeneous equation. The equation is proven to be homogeneous. However after using substitution of y=zx and its' derivative, I was not able to separate the variables conveniently as shown. Please advise. Thank you!

Here is the revised proof: Proof: Let f(x) = ax^3 + bx + c. Assume that f(x) has 3 distinct roots, f(p) = f(q) = f(r) = 0, there is a point x1 element of (p,q) such that f'(x1) = 0 ; x2 element of (q, r) such that f'(x2) = 0. Since ab < 0 then there are two possibilities where a>0 and b<0...

Hi, I have done up the proof for the question below. Please correct me if I have done wrong for the proof. Thanks in advanced!Question: Prove that if ab < 0 then the equation ax^3 + bx + c = 0 has at most three real roots.Proof: Let f(x) = ax^3 + bx + c. Assume that f(x) has 4 distinct...

Re: Using rolle's theorem to prove for roots Thanks, will change the usage of a and b accordingly.

I have deduce a proof as stated below and am not sure if it is correct, therefore need some advice. Question: Prove that if ab > 0 then the equation ax^3 + bx + c = 0 has exactly one root by rolle's theoremProof: Let f(x) = ax^3+bx+c = 0. f(x) is continuous and differentiable since it is a...

Hello, I have attached the question and the steps worked out. I am not sure if my steps are correctly. Need advise on that. Next, I am not sure how to show f''(0) exist or not. Thanks in advance!

Need help for the two parts! Thanks!

I am not sure what examples to give, need help on this. Have attached the theorem as well.

Need advice on how to find lim of cos(x) using the inequalities provided. Also part (b) for help. Thanks.

Hi, may I ask how do you know that f(U)⊆(1/2,3/2) and how do u know ε=1/2? How do I answer to the f(x) = 1 and 0? I am confused.

Not sure how to do this question. Help needed. Thanks

Appreciate the help needed for the attached question. Thanks!