Please help me with my homework

Please make sure you have a clear handwriting and label it with letters. Thank you.

Make sure you read the question carefully and answer all the question.

6.) Let f(x) = x^3 - 3x^2 + x +5/2x^3 - 16

a.) What are the horizontal asymptotes of f(x)

b.) What are the slant asymptotes of f(x)?

c.) What are the vertical asymptotes of f(x)?

d.) Plot f(x).

e.) Plot the asymptotes.

f.) Do yo ur asymptotes match your graph? (yes or no)

7.) Letf(x) = ln(x)*e^-x

a.) What are the horizontal asymptotes of f(x)?

b.) What are the slant asymptotes of f(x)?

c.) What are the vertical asymptotes of f(x)?

d.) Plot f(x).

e.) Plot the asymptotes.

f.) Do yo ur asymptotes match your graph? (yes or no)

8.) Find the limit as x --> -1 for

y = x^3 - 7x - 6/x^3 + 2x^2 - 5x - 6

a.) Using the graphical method, plot the function and find y(-1).

b.) Using L'Hopital's rule.

c.) By factoring the numerator and denominator. Hint: One of the factors is (x + 1).

d.) D o all three of your answers agree? (yesor no)

9.) Find the limit as x --> 0 for

y = 2^x - 1/x

a.) Using L'Hopital's rule.

b.) Using the graphical method. Show your graph as part of your answer.

c.) Do yo ur two answers agree? (yes or no)

10.) Given the function

y = ( 3/x + 1)^2x

a.) Find the limit as x --> +inf.

Hint: Find the limit of ln(y) first, then find limit of y = e^ln(y). Also change (3/x + 1) = 3+x/x.Remember: ln(M/N) = ln(M) - ln(N), and x = 1/[1/x]..

b.) Make a plot of y and your limit.

c.) Do es your limit and your asymptote match? (yes or no)