I have trouble with these can anyone help me work out this problem. lim e^((5x^2+sinx)/(x^2+20)) x-infinity Thanks in advance.
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Originally Posted by macro I have trouble with these can anyone help me work out this problem. lim e^((5x^2+sinx)/(x^2+20)) x-infinity Thanks in advance. ignore the exponent's base for a moment ... what is this limit? $\displaystyle \lim_{x \to \infty} \frac{5x^2 + \sin{x}}{x^2 + 20}$
it's 5 right since its the principle term?
Originally Posted by macro it's 5 right since its the principle term? correct. so, what is $\displaystyle \lim_{x \to \infty} e^{\frac{5x^2+\sin{x}}{x^2+20}}$ ?
Is the limit e^5 since its a constant?
Originally Posted by macro Is the limit e^5 since its a constant? yes, the limit is $\displaystyle e^5$ ... I don't know what you mean by "it's a constant" the limit is just a property of composite functions ... if $\displaystyle \lim_{x \to \infty} f(x) = 5$ , then $\displaystyle \lim_{x \to \infty} e^{f(x)} = e^5$
oh ok thanks a bunch
The crucial point is that $\displaystyle e^x$ is a continuous function: $\displaystyle \lim_{x\to a}e^{f(x)}= e^{\lim_{x\to a} f(x)}$.
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