Can I fill out the NIOS April 2018 stream 1 form by an offline form because the online form is closed and I want to appear on this stream to save this question?

You can contact your respective regional centers for this. Though on the website there is no where mentioned that the application form will be available offline. However, it is best to ask them regarding this.

How would you use LHopital's rule to show that the [math]lim_{x to 0} frac{(1 + frac{x}{2}) log (x + 1) - x}{x^3} = frac{1}{12}[/math]?

L'Hôpital's rule says that when we seek the limit of a ratio [math]f(x)/g(x)[/math], and substitution gives an indeterminate result of 0/0 (or [math]infty/infty[/math]), we can instead seek the limit of [math]f'(x)/g'(x)[/math]. Furthermore, if the limit is still indeterminate after applying that rule, we can do so repeatedly.Because this looks like a homework question, I’ll show the process but leave out the details of finding the derivatives and the algebra required to rewrite the expressions:[math]begin{align*}&phantom{={}}lim_{x to 0} frac{(1 + frac{x}{2}) ln (x + 1) - x}{x^3}& text{indeterminate (0/0)} &=lim_{x to 0} frac{(2 + x) ln (x + 1) - 2x}{2x^3} &=lim_{x to 0} frac{(2+x)frac{1}{x+1}+ ln (x + 1) - 2}{6x^2} & text{L'Hôpital #1} &=lim_{x to 0} frac{(x+1)ln (x + 1) - x}{6x^2(x+1)} & text{(still indeterminate)} &=lim_{x to 0} frac{ln (x + 1)}{18x^2+12x} & text{L'Hôpital #2} &=lim_{x to 0} frac{frac{1}{x + 1}}{36x+12} & text{L'Hôpital #3}end{align*}tag*{}[/math]After the third application of L'Hôpital’s rule, the resulting expression is no longer indeterminate, so the limit can be evaluated by direct substitution.How would you use LHopital's rule to show that the [math]lim_{x to 0} frac{(1 + frac{x}{2}) log (x + 1) - x}{x^3} = frac{1}{12}[/math]?

Is every prime number other than 2 and 3 of the form (6k±1)? Is this a proven result? What are other resources about it?

Every integer can be written in the form of [math]6n,6n+1,6n+2,6n+3,6n+4[/math] or [math]6n+5[/math].It is quite evident that [math]6n[/math] is always divisible by 6, 6n+1 may be prime, [math]6n+2[/math] will always be divisible by 2, [math]6n+3[/math] by 3, and [math]6n+4[/math] by 2. [math]6n+5[/math] may be prime. Our candidates for primality are therefore [math]6n+1[/math] and [math]6n+5[/math]. We can then see that [math]6n+5=6(n+1)-1=6x-1[/math] Therefore, every prime can be written in the form of [math]6n pm 1[/math]

I’ve been staying out of India for 2 years. I have an NRI/NRO account in India and my form showed TDS deduction of Rs. 1 lakh. Which form should I fill out to claim that?

The nature of your income on which TDS has been deducted will decide the type of ITR to be furnished by you for claiming refund of excess TDS. ITR for FY 2017–18 only can be filed now with a penalty of Rs. 5000/- till 31.12.2018 and Rs. 10,000/- from 01.01.2019 to 31.03.2019. So if your TDS relates to any previous year, then just forget the refund.

What is [math]lim_{w to -infty} frac{w^2 - 4w + 1}{3w^2 + 7w - 4}[/math]? This is a problem about indeterminate forms using L’Hôpital’s rule.

When calculating limits of dividing polynomials approaching infinity (either one), there’s a rule you can use. The Polynomial Growth rule. The monomial which bears the highest order will govern the entire curve’s growth, so you can neglect the rest and work with the highest-powered monomial.When you apply that rule to this particular limit, you’ll get:[math]lim_{x to infty} = frac{w^2}{3w^2}[/math]Which will give you 1/3. You don’t need L’Hopital’s rule to solve it. If using it is a requirement, though, Bruce Walden’s answer is the absolute way to go. Hope it helps.EDIT: Thanks to Robby Goetschalckx for making the equations look as they’re supposed to look, hahahaha. I haven’t mastered Quora’s math writing. If anyone is willing to offer a crash course I’d be very thankful.

How do I evaluate this limit [math]displaystyle lim_{xto0}left(frac{1}{log(x+sqrt{1+x^2})}-frac{1}{log(1+x)}right)[/math]? You are free to use L'Hôpital's rule.

One could do it with power series a bit easier than with L’Hospial’s rule.The point is that to second order in x the denominators are log(1+x) = x -x^2/2+… and log(1+x+x^2/2 + …) = x+x^2/2 -1/2(x+x^2/2)^2 +… = x+…So you get 1/(x+0x^2+…) - 1/(x-x^2/2+…) = (-x^2/2+…)/(x^2+…) which approaches -1/2.I am skipping details and justification, but hopefully you can fill them in.

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Understanding the CC 1355 Rule to Show Cause

The CC 1355 rule to show cause is a legal document used primarily in Virginia. It serves as a formal request for a court hearing, allowing a party to explain why a specific action should or should not occur. This form is essential in various legal contexts, including family law and civil disputes. Understanding its purpose and implications is crucial for those involved in legal proceedings.

Steps to Complete the CC 1355 Rule to Show Cause

Completing the CC 1355 form requires careful attention to detail. Here are the key steps:

Begin by entering the case number and the names of the parties involved at the top of the form.
Clearly state the reasons for the request in the designated section, providing specific details and any relevant evidence.
Include any necessary dates and deadlines related to the issue at hand.
Sign and date the form, ensuring that all information is accurate and complete.

Legal Use of the CC 1355 Rule to Show Cause

The CC 1355 form is legally binding once properly completed and submitted. It must adhere to specific legal standards to be considered valid in court. This includes compliance with local court rules and procedures. The form must be filed in the appropriate jurisdiction, and all parties involved should be notified of the proceedings.

Required Documents for the CC 1355 Rule to Show Cause

When filing the CC 1355 form, certain documents may be required to support your request. These can include:

Any previous court orders relevant to the case.
Evidence supporting your claims, such as affidavits or witness statements.
Proof of service to demonstrate that all parties have been notified of the filing.

Examples of Using the CC 1355 Rule to Show Cause

The CC 1355 form can be utilized in various scenarios, including:

Requesting a modification of child custody arrangements.
Seeking enforcement of a court order related to child support.
Challenging a decision made by the court that affects the parties involved.

Filing Methods for the CC 1355 Rule to Show Cause

The CC 1355 form can be submitted through various methods, ensuring accessibility for all users. Options include:

Filing in person at the local courthouse.
Submitting the form via mail, ensuring that it is sent to the correct court.
Utilizing online filing systems if available in your jurisdiction.

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CC 1355 RULE to SHOW CAUSE PAGE 1 USING THIS FORM 1

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Understanding the CC 1355 Rule to Show Cause

Steps to Complete the CC 1355 Rule to Show Cause

Legal Use of the CC 1355 Rule to Show Cause

Required Documents for the CC 1355 Rule to Show Cause

Examples of Using the CC 1355 Rule to Show Cause

Filing Methods for the CC 1355 Rule to Show Cause

Quick guide on how to complete cc 1355 rule to show cause page 1 using this form 1

Effortlessly Prepare CC 1355 RULE TO SHOW CAUSE PAGE 1 USING THIS FORM 1 on Any Device

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