Use lhopitals rule to evaluate the limit and evaluate the

Question

Question 1- Use L'Hopital's Rule to evaluate the limit:

a) lim_x→∞(x tan (3/x))

b) lim_{x→ 0}⁺(1+(3/x))^x

Question 2- Evaluate the improper integral (or state "divergent"). Justify your answer completely.

a) ₁∫^∞ x·e^-3x dx

b) _-1∫¹ (1/3√x) dx

Question 3- Use partial fraction to integrate:

∫(4x² - x + 12/x³ + 4x)dx