Evaluate the limit using L\'Hospital\'s rule if necessary Evaluate the limit usi

Question

Evaluate the limit using L'Hospital's rule if necessary

Evaluate the limit using L'Hospital's rule if necessary.

Answer:

Find the limit: lim x rightarrow 0 (4/x - 4/sin(x)) = Evaluate the limit using L'Hospital's rule if necessary lim x rightarrow (1 + 12/x)1/4 Compute the following limits using l'Hopital's rule if appropriate. Use INF to denote infinity and -INF to denote - infinity limx rightarrow 0 1-cos(4x)/1-cos(5x) lim x rightarrow 1 6x - 5x - 10(x2 - 1) Evaluate the limit using L'Hospital's rule if necessary. lim x rightarrow 0+ x3sin(X)

Explanation / Answer

1)

lim = 4(cosx - 1)/(sin(x) + x.cos(x)) = 4sin(x)/(2cos(x)- x.sin(x)) = 4*0/2 = 0

2)

lim = e^(12/4) = e^3

3)

lim = 4sin(4x)/5sin(5x) = 16cos(4x)/25cos(5x) = 16/25 = 0.64

4)

lim = 6-5-0 = 1

5)

y = x^(3sinx) -> ln(y) = 3sin(x).ln(x) = 3ln(x)/csc(x)

lim ln(y) = (3/x)/(-cos(x)/sin^2(x)) = 0

-> lim y = lim x^(3sinx) = e^0 = 1

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.