Evaluate the following limits: -5x - e* Lim -40 12 sin x i. lim x → 00 ii. x-4,

Q: 1 lim x –1 e – e

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Q: For which sign, + or −, does the following limit exist?

A: First find the limit for the + sign. if the expression is 00 then apply l' hopital rule.…

Q: Use l'Hôpital's Rule to evaluate the limit. .3 8x +7 2, lim X- 1 X1 O A. 11 O B. 19 C. O C. - 16 D.…

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Q: Explain why the following limits of (a) and (b) do not exist. (a) lim - x→1x-1 sin x (b) lim x→1…

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Q: calculate the following limits (a) lim x->0 (e^x-1)/(sinx) (b) lim x->0^+ xlnx

A: Part(a) Given limit

Q: Find the limit. 2 lim 1 x-0 00 O 2 O 000

A: Let,

Q: Find the indicated one-sided limits, if they exist. (If an answer does not exist, enter DNE.) f(x) =…

A: As given Function  fx=-x+6if x≤05x+5if x>0 Thus limx→0-fx=limx→0--x+6             =6

Q: Find the following limits i 1. 8x lim x>+* 5x – 7

A: According to bartleby guideline we only do the first part

Q: Evaluate the following limits, where c and k are constants.

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Q: Find the following limit. x2 + 16 lim (x, y) → (0, 18) arctan x² + (y – 18)2,

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Q: Determine the following limits: 2x +3 [a] lim b lim 0 4x-4 sin x

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Q: Evaluate the following limits. a. lim 2x 3x² b. lim x→0+ e-3/x ,2 X² ||

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

A: The given expression is limx→ 0ex-1+xe-x-1-x

Q: Find the following limits : 1+2 +3+...+x 4) lim X00 x2

A: Ans:  We have to Evaluate  the limit              limx→∞ 1+2+3+‐‐‐+xx2

Q: For which sign, + or - , does the following limit exist?

A: Given that, limx→01x±1x(x-1) Consider, limx→01x+1x(x-1) = limx→01x1+1x(x-1)1x…

Q: Use l'Hôpital's rule to find the limits x- 2 7. lim X2x - 4 x? - 25 8. lim -s x+ 5

A: l'Hospital rule is used when the value of the function is not defined by directly substituting the…

Q: Compute the following limits and write your answer to the boxes. lim 9x cot 8x 6x? lim x2 18x 60 - |…

A: Solve by limit

Q: Evaluate the following limits analytically: x-2 a. lim- x-1x2+x-6 10-x-4 b. lim x--6 x+6 c. lim *+13…

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Q: Q3: (a) find the following limits if exist:- (1) limx-o √x+9-3 1-cosx xsinx (2) limx-07 (3) limx-1…

A: Topic = Limits

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

A: Given: limx→5 x2+11-6x2-25

Q: Find the following limit: 2x –x+3 lim 3.x +5

A: Explanation of the solution is given below...

Q: Find the following limits if they exist. 1. 2 3. lim x→+0 5x – 7 8x 4x +1 lim X +2 +x + 27 lim -7 2…

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Q: Evaluate the following limits. If needed, enter oo for o and oo for V3 + 9x2 (a) lim 5 + 6x 3+ 9x2…

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Q: lim (sec x)cot x X-

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Q: Evaluate the following limits. If needed, enter oo for o and -oo for – 0o. (a) lim (– 40æ² – 36x³) :…

A: Given(a)limx→∞(-40x2-36x3)replacing limit=-40(∞)2-36(∞)3 as we know power of infinite is…

Q: Find the following limits if they exist. Must show all work (analytically?): 1. X-2 lim (x) where…

A: Given that: 1. limx→-2f(x), where f(x)=-3x2+8, if x<22x,          if x>-2   NOTE: As per our…

Q: Find the limit. lim (2 – x)3 tan(a) x→1

A: limit

Q: Evaluate the following limits. If needed, enter oo for o and -oo for -o. 15x (a) lim - 2x 3 + 15x…

A: Use left hand and right hand limit concept

Q: Evaluate the following limits.

A: We have to find

Q: Evaluate the following limits analytically: x-2 x-1x2+x-6 a. lim 10-x-4 b. lim X--6 x+6 c. lim *+1 3…

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Q: Determine the value of the following limits, if they exist. If infinite, specify either o or -o. (If…

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Q: Evaluate the following limits. 2x2 - 3x +1 2x +1 (a) lim (5+ h)? – 52 (b) lim (c) lim In(sin(x))

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Q: Determine the following limits, using oo or-0o when appropriate, or state that they do not exont…

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Q: 1. lim e7x+2 X→-∞

A: "Since, you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q1/ Find the following limits. 1. lim x*+3x-4 2. lim x*- 16 x-1 2 X+2

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Q: Use formulas (3)–(5) to evaluate the limit.

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Q: Find the following limits if they exist. lim(xvx* +1-x*) lim( x+e*

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Q: Evaluate the following limits. If needed, enter oo for oo and -oo for – 0. V5 + 6x2 (a) lim 3+ 10x…

A: Use the substitution and then simplify the limit.

Q: + 34, find f '(x) using the definition f '(x) = lim h→0

A:

Q: 2) Find the following limits if they exist. a) lim xVx* +1-x lim(x+e')% b)

A: We have to find out limit

Q: Evaluate the following limits. If needed, enter oo for o and -oo for o, and DNE if the limit does…

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Q: + 1for all positive x-values, then what is lim f(x)? X+ 4

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Q: Find the limits of the following: A. lim X-3 B. lim x sin-

A: A. Let L=limx→3x-21x+13 ⇒L=limx→3x-2x+33x        =limx→33x(x-2)x+3        =3(3)(3-2)3+3…

Q: Find the following limits analytically or state that they do not exist. 2x+1 3. lim- x+0 x2+1

A: Given:limx→02x+1x2+1

Q: Determine the following limit. sin x lim x0 X + 16

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Q: Find the following limits when they exist: 1. lim g(x)   x to 1

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Q: Determine the following limits. x* + 7 lim x + x - x xSo

A: Given: limx→∞x4+7x5+x2-x Now we divide by the highest denominator power we get,…

Q: Evaluate the following limits: 1-sinx a. lim X→n1-cosx x²-49 b. lim x→7 x-7 C. lim X00 x2+1

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Q: Determine the values of the following limits. lim 2a? 2x + 4 lim %3D む+1 lim I -1 x -1

A: To find the value of the following limits.

Q: 1-sin x 18. lim TL X- 2.

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.