if a < -6 Let f(x) = | 2x + 13, if x > -6 Calculate the following limits. If the limit doesn't exist but it makes sense to call it o∞ enter Infinity , for –0 enter - Infinity ; in other cases where the limit does not exist enter DNE . lim f(x) = I-6 lim f(r) = lim f(x) = I-6

Q: Sx² – 4 if r 3 (a) lim f(r) - (b) lim f(x) = (c) lim f(r) = 3-

A: see 2nd step

Q: 4x-y<-1

A: Given  4x-y&lt;1 Can be rewritten as y&gt;4x-1 So we take the area above the line y = 4x -1 And all…

Q: I need to simplify the function algebraically to determine the limit. I know the initial…

A: Recall: Limit of a function :               Let f(x) be a function defined on an interval that…

Q: 16. Determine lim f(x) if the given function is x→2 f(x) = { 1², I 8-2x, if if x 2

A:

Q: Find the value of the limit: 3 tan(4x)– 12x lim

A: From the given problem:   limx→03tan4x-12xx3   This problem can be solved by the series expansion of…

Q: Ouestion 3 A. Evaluate the following limits: i. lim (3 + x)² - 9 ii. lim x² – 25 5-x iii. lim 5x+6x²…

A:

Q: 5. Evaluate the following limits: (a) lim Inr xxx (b) lim In r →1-1

A:

Q: 12 if x 3 х — 5 Compute the limits and determine the function value. Write "DNE" if the limit does…

A:

Q: Find the limits

A: limx→-∞tan-1x

Q: Find the following limits if they exist. Must show all work (analytically?): 1. lim f(x) where f(x)…

A: We will find out the limit of given function.

Q: (x - 3)2/3 lim r3 x2 +4x - 21

A:

Q: sin 2x lim

A: Consider the given function, limx→∞sin2xx since is a continuous periodic function, as sin2x∈-1,1. as…

Q: 2. lim g(x) for g(x) = { (-6x + 2x if x <-2 3x2 – 3 X--2 if x 2 -2

A: The given function is g(x)=-6x+2xif x&lt;-23x2-3if x≥-2 We have to find the limx→-2g(x)

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.