Reducing Sqrt(4t^2+4+1/t^2): Calculus Problem Help

In summary, the conversation discusses a calculus problem involving the expression Sqrt(4t^2+4+1/t^2). The equation for reducing this expression is provided, along with the steps for solving the problem using the chain rule. The significance of this problem in calculus is also mentioned, as well as the fact that it can be solved using various methods. However, reducing and applying the chain rule is the most efficient method. Common mistakes to avoid while solving this problem are not reducing the expression and not paying attention to the signs and exponents of the terms.
  • #1
snoggerT
186
0
reducing sqrt(4t^2+4+1/t^2) to (1+2t^2)/t




The Attempt at a Solution


- This is actually just a portion of a calculus problem, but I can't figure out how the book did the algebra here. I get (2t^2+2t+1)/t and don't know how that reduces to (1+2t^2)/t. Please help.
 
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  • #2
Factor the 1/t^2 out as 1/t. Then 4*t^4+4*t^2+1=(2*t^2+1)^2.
 
  • #3
Put the whole thing under a single fraction : (4t^4 + 4t^2 + 1) / t^2
Now above you have a complete square so you can simplify this and when you do the square root you get the exact solution
 

FAQ: Reducing Sqrt(4t^2+4+1/t^2): Calculus Problem Help

What is the equation for reducing Sqrt(4t^2+4+1/t^2)?

The equation for reducing Sqrt(4t^2+4+1/t^2) is Sqrt(4t^2+4+1/t^2) = 2t + 1/t .

How do I solve this calculus problem?

To solve this calculus problem, you can follow the steps of reducing the expression and then applying the chain rule to find the derivative. The final answer will be the derivative of the reduced expression.

What is the significance of this problem in calculus?

This problem is significant in calculus because it combines the concepts of simplifying and differentiating expressions, which are fundamental skills in calculus. It also helps to develop the understanding of the chain rule and its applications.

Can this problem be solved using any other methods?

Yes, this problem can be solved using various methods such as using the quotient rule, integrating the expression, or using the power rule for derivatives. However, reducing and applying the chain rule is the most efficient and straightforward method for solving this problem.

What are the common mistakes to avoid while solving this problem?

One common mistake to avoid is not reducing the expression before differentiating, which can lead to a more complicated and incorrect answer. It is also essential to pay attention to the signs and exponents of the terms while reducing and differentiating the expression.

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