I need some help with a Limit

[Vincent_M05]

Ok so I broke down the limit into 2 parts, in the U part, and in the V part I was really confident when I calculated the Limit for U and V and I thought that the +1 that was left would not bother me since it would just add 1 to the limit so 6-->7 but when I looked up the answer it was e^6. I am really stuck right now and I don't know why this would be the right answer, it 1:50 AM right now, so this could explain why I am so stuck on this question or I just have no clue what is going on since I have started learning about limits 3 days ago. I will attach my notes to this Thread and I would appreciate any help. Thank you!

 

[BigBeachBanana]

The [imath]2x[/imath] is in the exponent, not multiplication.
Rewrite the limit using exponential of logarithmic function and power rule:
[math]\lim_{x \to \infty}\left(1+\frac{3x}{x^2+2}\right)^{2x}= \lim_{x \to \infty}e^{2x\ln\left(1+\frac{3x}{x^2+2}\right)}[/math]

 

[Vincent_M05]

Ohh..., ok thank you very much?

 

[Vincent_M05]

The [imath]2x[/imath] is in the exponent, not multiplication.
Rewrite the limit using exponential of logarithmic function and power rule:
[math]\lim_{x \to \infty}\left(1+\frac{3x}{x^2+2}\right)^{2x}= \lim_{x \to \infty}e^{2x\ln\left(1+\frac{3x}{x^2+2}\right)}[/math]

Thank you very much?. Could you give me a link for a website that explains about that topic (exponential of logarithmic function and power rule), that would be nice.

 

[BigBeachBanana]

Thank you very much?. Could you give me a link for a website that explains about that topic (exponential of logarithmic function and power rule), that would be nice.

Since you're doing limits, I assume that you have been taught logarithms and exponents before. But if you need a refresher, here are some links:

Working with Exponents and Logarithms

The exponent of a number says how many times to use the number in a multiplication. ... In this example 23 = 2 2 2 = 8 ... (2 is used 3 times in a multiplication to get 8)

www.mathsisfun.com

Logarithm Rules

Learn the eight (8) log rules or laws to help you evaluate, expand, condense, and solve logarithmic equations. Try out the log rules practice problems for an even better understanding.

www.chilimath.com