Find the limits in Exercises 1–6.
3. lim(x→0⁺) (cox(√x))^(1/x)

3. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?

e. x ln(x)

3. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?

g. x^3 e^(-x)

4. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?

g. (1.1)^x

23. What roles do the functions e^x and ln(x) play in growth comparisons?

113. The function f(x) = e^x + x, being differentiable and one-to-one, has a differentiable inverse f^(-1)(x). Find the value of df^(-1)/dx at the point f (ln 2).

If $f\(\left\)(x\(\right\))=x^3-8x+6$, find the differential $dy$ when x = 2 and $dx = 0.2$.

If $f\left(x\right)=\sqrt{x+2}$, find the differential $dy$ when $x=2$ and $dx=0.01$.