Using the ε − N definition of a limit, prove that lim(n→∞)=(6n^3 −2n+1)/(2n^3+1)=3.

Q: Evaluate lim f(x), lim f(x), and lim f(x) at the point a = 5, if the limits exist. (If an answer…

A: Given function : f(x) = 10 -x  if x ≤5 f(x) = x + 3 if x > 5

Q: evaluate the limit lim (x + 1)(3x^2 − 9) x→2

A:

Q: Consider lim e-. a) lim 4x - x² = 0 b) If we let t = 4x - , then we can rewrite the limit as lim of

A:

Q: How does the sandwich theorem enable us to calculate a variety of limits?

A: Sandwich theorem: Consider 3 function f(x),gx,hx such that fx≤gx≤hx. Also, assume that limx→cf(x)=L…

Q: Find the limit of  limitx->0= x2+4,

A:

Q: What is the limit when x is approaching negative infinity when the function is (8x+2) / (4x-5)

A: Given

Q: Evaluate the limit using L'Hospital's rule 1 lim 3xe 3x

A:

Q: limx→∞42x3+2x2-2x/353+x2+4X+5=   What is the limit?

A: Given expression is We need to find the limit.

Q: b) limx-2+ 72-4 x²– 4

A: To evaluate: limx→2+x-2x2-4

Q: Find the limits 2 lim x0* 3x'/3

A: Given: limx→0+23x13  ……1

Q: Evaluate the limit 2x + 4 lim I→ 0 3x2 - 7x + 7

A: Given

Q: How do it find the limit as b approaches 8?

A: Here we need to find the limit value of the given function where b tends to 8.

Q: \Find the limit: lim x¹/Inx 818

A:

Q: By using the e- & definition, show that lim 2² + X 4 = 1.

A: By the €-δ definition of limit,

Q: what is the limit as x goes to infinity of (1-(4/7)^x)/(7-4(4/7)^x)?

A: Given function is