Provide all necessary steps to find the limit of the following functions: (a) lim csc X – cotx (i) Iig (- ला) 1. tan-1 (1 +9* bx (c) lim (d) (2 – 2x)*an() etx -1- 4x (e) lim x2

Q: Only one of these calculations is correct to evaluate the limit lim x

A:

Q: Determine the limit by sketching an appropriate graph. V16-x2 Osx< 4 lim f(x), where f(x) = 4 4sx<8…

A: GRAPH

Q: Find the one-sided limit (if it exists).

A: We will find the limit numerically  Let, x y -0.1 -5.0000025 -0.01 -50 -0.001 -500…

Q: Find a Limit using factoring:

A: We have to find the limit using factoring: limx→1x2+2x-3x-1 This is 00 indeterminate form of limit.…

Q: Find the limit (if it exists). If it does not exist, explain why.

A:

Q: Find the one-sided limit (if it exists).

A: Given: Find the one-sided limit (if it exists).

Q: Find the limit, if it exists.

A: Consider the given: limx→∞ x21−8x2Divide numerator and denomintor by "x2",limx→∞ x21−8x2=limx→∞…

Q: Evaluate the limit sin 2x lim 20 7x

A:

Q: Create a table of values for the function and use the result to explain why the limit does not…

A: Given: Function  Consider few values less than 0 and few values greater than 0 Then evaluate…

Q: Find the one-sided limit

A: Given: limx→2+ xx-2 To Find: To evaluate the given limit.

Q: Find the limit. lim_ (x² + 2x) x--2

A: Solution

Q: Evaluate the limit sin 2x lim 7x

A: limx→0 sinxx = 1

Q: Find the limits limx→ -∞tan-1 x

A:

Q: evaluate the limit.

A:

Q: The value of the limit x42x-3 lim メー)イ X-イ

A: Given : limx→1x2+2x-3x-1

Q: 3. lim Jx| ズート-1

A: Let's find.

Q: 2. Find the limit of the following function lim (secx- tan x)

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: Evaluate the limit sin 3x lim 5x

A:

Q: Create a table of values for the function and use the result to explain why the limit does not…

A: To create a table of values of x for the function limx→02x3, take the values of x nearer to 0, that…

Q: Find the limit using table: 1-cosx lim- X-0 x -0.1 -0.01 -0.001 0.001 0.01 0.1

A:

Q: Find the one-sided limit (if it exists).

A: Given: limx→0+x-1x+3 for evaluating given limit, we put x=0+ in given limit

Q: Evaluate the limit sin 3x lim 9x

A:

Q: Find the one-sided limit (if it exists).

A: Given: limx→0-sec x32x

Q: How do you solve question 11 and 12?

A: (11)Given:

Q: Find the limits

A: limx→-∞tan-1x

Q: Find the limits lim tan-x X-

A: Solution: consider the given limit function; limx→-∞tan-1x Let  tan-1x = y⇒tan y = x when x → -∞…

Q: Find the indicated limit algebraically. Show complete solution. 2x -x-3 1. lim x--1 2. lim () x+1…

A: Solution: Consider the given limit function is limx→-12x2-x-3x+1 We can factorized numerator and…

Q: Find the limit. sin(x - 5) lim x* + 4x - 45

A: Given : limx→5sinx-5x2+4x-45

Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

A:

Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim x→1 x´ +x –2 2

A:

Q: Find the limit (if it exists). If it does not exist, explain why.

A: limx→0-xx

Q: Find the one-sided limit (if it exists).

A: We will find the limit numerically.

Q: Find the limit by using l'Hôpital's Rule. ( limx-14³-x-3

A:

Q: Find the one-sided limit (if it exists).

A:

Q: Find the limits of the functions below a) limx-3 x* sin x b) lim,

A: We can find the limit of both the question as below.

Q: Use the definition of the derivative to evaluate the limit. (6 + h)** - 1296 lim

A: Given limit is : limh→06+h4+h-1296h To find the value of limit.…

Q: Find the limits lim x→1- sin-1x

A:

Q: Calculate the limit.

A: limx→∞tan-11+x1-x

Q: Evaluate the limit  Limx-&gt;0 (ex-1-x)/x3

A:

Q: In(x²) lim 7x

A: Given: limx→∞lnx27x we know that lnmn=nlnm so, limx→∞lnx27x=limx→∞2lnx7x=27limx→∞lnxx  ∞∞form we…

Q: Use the graph to evaluate the limit. lim lim Find x-(-1) f(x) and X-(-1)+ f(x)

A: Consider the first given limit: This means that when x is approaching to -1 from left side then…

Q: Estimate the value of the limit lim→0 tan x by filling out this table and then making an educated…

A: Graphing utility table

Q: Find the limits

A: Consider the following limit: limx→0tanx=tan0=0

Q: Find the limit. lim sech(x)

A: Given:limx→∞ sechx

Q: Evaluate the limit. In x lim x -1 sin 8TX

A:

Q: Find the limit if it exists. lim (2x+3) X--2

A:

Q: Find the one-sided limit (if it exists) lim 9x tan TX x-(1/2)*

A:

Q: ■ Find the limit.

A: To evaluate the limit: limx→2π-x cscx Solution: We know that limx→2π-sinx=0- Now, evaluating the…