Evaluate these limits (show your work, and use L'Hopitaľ's Rule on the first one): · Inx lim x1x2-1 lim 3 x2+x-2 2-4x-5x3 lim x- 00 x3+3x-10

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

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: Use l’Hospital’s rule where applicable to find each limit.

A: According to L'Hospital's Rule,if we have an indeterminate form 00or ∞∞ then we will differentiate…

Q: Use the definition of the limit of a function of two variables to verify the limit.

A:

Q: Find the one-sided limit

A: To find:limx→-4- x2+2x+4

Q: Find the limit, if it exists.

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

Q: find the limit or explain why it does not exist. 1 - Vx lim 1- x

A: we have to find the limit . limx→11-x1-x

Q: Evaluate the limit: lim (x - Inx)* x→0+

A: Using limit definition

Q: Give the two-step method for evaluating a limit of the form lim f(x)8(x).

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 limit if it exists. lim Vx² – 9 x→3+

A:

Q: 2 lim x→1- x²

A: The limit of the function f(x) is obtained as L=limx→a-f(x)L'=limx→a+f(x) Then the limit of the…

Q: use definition of limit to show:   lim    (4x + 1) =13 x-&gt;3

A: The definition of limit:

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

A: Solution

Q: Use l’Hôpital’s Rule to find the limits

A:

Q: 1 lim xー→1*(x-1 Inx

A: Limit of a function:          The  limit of a function f(x) exists if and only if the one sided…

Q: Verify that L’Hôpital’s Rule applies and evaluate the limit.

A: Consider a function fx. The limit of a function at x=a is given by: limx→a fx=fa

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: x -1- V3x +1 V3x + 1 lim x-5 x - 5

A:

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

A: Given:limx→2-x2x2+4=limx→2- x2limx→2- x2+4=2222+4=48=12

Q: find the limit or show that it does not exist for lim x→−∞ √4x2 + 1 / 2x + 5 .

A: limx→-∞ 4x2+12x+5 = limx→-∞ x4+1x2x2+5x                                =limx→-∞ 4+1x22+5x…

Q: Use l’Hôpital’s rule to find the limits

A: Given: limx→π2lncosecxx-π22 for evaluating given limit, in given limit we substitute x=π2+h so,…

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 limits limx→1+x1/(x-1)

A: limx→1+xx-1

Q: a) lim 3x2-10x5

A: Find the limit of 3x^2-10x^5 at - infinity

Q: When trying to explain an infinite limit. What does it mean to say that: lim as x approaches 0…

A:

Q: Evaluate the limit using L'Hospital's rule et + 3x – 1 - lim x →0 9x

A: To find :-

Q: Evaluate the limits by previous methods or by L'Hospital's Rule, if applicable: a) lim- X- sin x -X…

A: We have to find the limits of the given following conditions

Q: x + 2 x 3 12 - 3.

A: since you have asked multiple questions in single request so we will be answering only first…

Q: Use the theorems to evaluate the limit. 1 lim x → ∞ x2 ||

A: We have to evaluate the limit.

Q: Use the theorems to evaluate the limit. 1 lim x →∞ X² ||

A:

Q: Find the limit. (a) lim x→3 Vx +6 – x x3 – 3x2

A:

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

A: We will find the limit numerically.

Q: Find the limit using direct substitution. 3x + 2 lim x-1 1-X 1 -x

A:

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

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 l’Hôpital’s rule to find the limits

A: We have to find the limits using L' Hospital's rule: limx→-5x2-25x+5 Since it is 00 form so we can…

Q: Use l’Hôpital’s rule to find the limits

A: The expression limx→03x-12x-1. We have to find the limit of this given expression by using…

Q: Find the limit or show that it does not exist. Vī lim 1+4x6 2- x'

A: To find the limit: limx→ -∞ 1+4x62-x3

Q: Evaluate the limits. If a limit does not exist, enter DNE. |x + 15|| lim x--15* x + 15 |x + 15|| lim…

A:

Q: 3 lim - 1 x² + x – 2) X-1

A: By L'Hospital 's Rule limx→1 (xx-1 - 3x2+x-2) =limx→1(x(x2+x-2)-3(x-1)(x-1)(x2+x-2))…

Q: Find the limit or show that the limit does not exist. lim→-0 4x2 + 3x + 2x x→-∞

A: See the details solution in below

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

A:

Q: use l’Hôpital’s Rule to evaluate the limit

A: Given limit is limx→1x3-14x3-x-3.

Q: x - 27 a) lim 4x - 3x² - x +3 b) lim x-+3 X-3 X-1 1 1 x+8-2 c) lim d) lim X2 X+2

A:

Q: Prove the limit. Using the precise definition of a limit. lim x approaches 2 x3 =8.

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Q: Evaluate the limit lim Va x + 3x + 11 – x 2 -

A:

Q: Evaluate the limit lim x² + 4x – Vx² + x ) and interprete the result in relation to x 00…

A:

Q: Evaluate the limit: lim Væ+5-V5 x-0

A:

Q: x +1 lim а—1 х2 — 1 x-

A:

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.