Determine the following limits. 

lim x→−∞ (2x^-8 + 4x³)

Determine the following limits.

a. lim x→1^+ x / |x − 1|

Determine the following limits.

c. lim x→1 x / |x − 1|

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→1 5x^2 + 6x + 1 / 8x − 4

Determine the following limits.

a. lim z→3^+ (z − 1)(z − 2) / (z − 3)

Determine the following limits.

a. lim x→−2^+ (x − 4) / x(x + 2)

Determine the following limits.

b. lim x→−2^− (x − 4) / x(x + 2)

Determine the following limits.

c. lim x→−2 (x − 4) / x(x + 2)

Determine the following limits.​

lim x→5 x − 7 / x(x − 5)^2

Determine the following limits.

a. lim x→2^+ x^2 − 4x + 3 / (x − 2)^2

Determine the following limits.

lim x→−5^+ x − 5 / x + 5

Determine the following limits.

b. lim t→−2^− t^3 − 5t^2 + 6t / t^4 − 4t^2

Determine the following limits.​

lim x→3^- x − 4 / x^2 − 3x

Determine the following limits. 

lim x→−∞ 40x^4+x^2+5x / √64x^8+x^6

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→2 (5x−6)^3/2

Determine the following limits. 

lim x→∞ 6x²/(4x^2+√(16x⁴ + x²))

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→1 x^2 − 1 / x − 1

Determine whether the following statements are true and give an explanation or counterexample.

a. The value of $\underset{x\to 3}{\lim }\frac{x^2-9}{x-3}$ does not exist.

Determine whether the following statements are true and give an explanation or counterexample.

d. $\underset{x\to 0}{\lim }\sqrt{x}$ . (Hint: Graph y=√x)

Determine whether the following statements are true and give an explanation or counterexample.

e. $\underset{x\to \frac{\pi }{2}}{\lim }\cot x=0$ . (Hint: Graph y=cot x)

Determine the following limits. 

lim x→−∞ (x+ √x^2−5x)

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→4 x^2 − 16 / 4 − x

Postage rates Assume postage for sending a first-class letter in the United States is $0.47 for the first ounce (up to and including 1 oz) plus $0.21 for each additional ounce (up to and including each additional ounce).

a. Graph the function p=f(w) that gives the postage p for sending a letter that weighs w ounces, for 0<w≤3.5.

Assume postage for sending a first-class letter in the United States is $0.47 for the first ounce (up to and including 1 oz) plus $0.21 for each additional ounce (up to and including each additional ounce).

b. Evaluate lim w→2.3 f(w).

Determine the following limits. 

lim x→−∞ (e^x cos x +3)

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→b (x − b)^50 − x + b / x − b

Evaluate each limit and justify your answer. 

lim x→0 (x / √16x+1-1)^1/3

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→−1 (2x − 1)^2 − 9 / x + 1

Complete the following steps for each function.

c. State the interval(s) of continuity.

f(x)={x^3+4x+1 if x≤0

2x^3 if x>0; a=0

Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.

lim x→9 √x − 3 / x − 9