Question

Calculus BC
A screenshot of the problem is attached.

Answer 1

Use properties of Logarithms to simplify the limit:

`\lim_(x \to \0^+)`e^3/x(e^x+x)

Move the limit to the exponent:

e^x
`\lim_(x \to \0^+)`3/xln(e^x+x)

Rewrite as:

e^x
`\lim_(x \to \0^+)`3ln(e^x+x)/x

Move 3 outside the limit and applay L'hospitals rules to get the final answer e^6