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Question
Evaluate the given limit in the image
)
Evaluate the natural log of this limit , then raise e to your answer.
ln[(x^2+5x+6)/(x^2+2x+3)]^x = xln[(x^2+5x+6)/(x^2+2x+3)] =
ln[(x^2+5x+6)/(x^2+2x+3)]/ x^-1
use L'Hospital's Rule and simplify to find
lim ln[(x^2+5x+6)/(x^2+2x+3)]/ x^-1 = lim (3x^4+6x^3-3x^2)/(x^4+7x^3+19x^2+27x+18) = 3
The answer is therefore e^3
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Calculus
Answers by Expert:
Socrates
Expertise
I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.
Experience
Ph.D. in Mathematics and many years teaching Calculus at state universities.
Education/Credentials
B.S. , M.S. , Ph.D.
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