I. Evaluate the following limits or justify why they do not exist. 2х- 6 lim %3D a. x→3 x² - 3x sin x b. lim x→0.3x² +4x %3D с. lim x(1-x)_ x→1

Q: Determine the following limits analytically.

A: Given: L=limx→-1x2+8-5-4xx3+1 For evaluating given limit, we substitute x=-1+h, h→0 So,…

Q: Q2) find the value of each limit sint 1) lim(- 1+cost +tcost C+cost x+xcosx 2) lim 0 sinxcosx

A: The limits of given functions are given as follows :

Q: Q4)A) Find the following limits (for two only). x+1 1. limx→-1 х2-х-2 1-Vx 2. limx→1 1-x 2х 3.…

A: Part 1,Given,           limx→-1x+1x2-x-2

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

A: Part(a) Given limit

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A:

Q: Verify the limits in a given equation below. (x+h)²-h² lim X→0

A: Verify itx→0lim(x+h)2-h2x

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A: limit values=?

Q: Suppose that on the interval (2,5) f(x) less than or equal to g (x) less or equal to h (x) and Lim…

A: We have the following information.

Q: TX-1 t. Lim ×つ○ 1

A: limx→0 πx-12x2    +πx(e2πx-1)=limx→0 πe2πxx-πx-e2πx+1+2πx2x2 (e2πx-1)   limx→0 πx-12x2…

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A:

Q: x³ - 8x* +1x lim xa -5-14

A: Dear student our policy is to answer first one only in case of multiple question kindly repost the…

Q: Assuming h > 0, compute Vx - Vh lim x→h X-h (a); Vh (b). 2h (c) (d) 2h (0)

A:

Q: Find the limits limx→q(ln x)1/x

A: Given,     limx→qln x1x

Q: Verify the limits in a given equation below. (2х-4)2 lim X→3 x+1

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Q: sin x – x (a) lim (b) lim (1+ x)/* 1/x

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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: Evaluate the limit. lim     In (Sinh x)x →0+

A: we have to evaluate the limit. lim     In (Sinh x)x →0+

Q: Determine the value of the following limit. sinh(x) = x lim - x3

A: Given that limx->0 sinhx-xx3

Q: Find the following limits. Do not apply L'Hospital's rule. ペ-4 lim +2 |x– 2| (i) (ii) sin (3t) lim

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Q: Use the Squeeze Theorem to prove lim = 0. x00 x+ e- For x 0, since 0 < e* <1, we have

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Q: If 3x s f(x) sx +2 for 0sxs 2, evaluate lim f(x).

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Q: lim (sec x)cot x X-

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Q: 2. lim (e* – 1)lnx X0+

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Q: e) lim x*十

A: Find the attachment

Q: bx a (c) lim| 1+

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Q: Evaluate the following limits: V10 + 6х — 2 (a) lim x→-1 x2 – 2x – 3 1 – sin(x) (b) lim x→5 (2x –…

A: Use l hospital rule for finding the limit.

Q: Use the graph to compute the quantities asked for. y lim, 3 f (x) does not exist -1

A: our objective is to find the limit

Q: Find the value of the positive constant c such that....

A: Given- limx→∞x-cx+cx=14 To find- The value of c. Concept Used- If any limit of the function fxgx in…

Q: 3x 3. lim х-0 sinx

A:

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

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Q: O Determine the following limits O limx-0 3 1+y3x+1 sin 2x limx-0 10x"+x*+31 limx-too

A: We are allowed only 3 subparts of a question

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

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Q: Use l’Hospital's Rule to show that lim 1+ X. = e. コ

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Q: Find the limits limx→0+x (ln x)2

A: Consider : limx→0+x(ln2x). Modify the limit function. limx→0+(ln2x)1x…

Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. - x – 20 lim…

A: Here we have to evaluate the limit of given function

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

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

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

A: We are given two limits to evaluate.  Both of them are of inderminate forms.

Q: 1 lim \3 Vx + 9/

A: Rationalization of an expression is done to remove the radical expression from the term. For…

Q: Find the following limits. Do not apply L'Hospital's rule. 2-4 lim +2 x– 2| (1) (ii) sin²(3r) lim…

A: According to question given:(i) limx→2x2-4x-2When x approaches 2 from right x-2=x-2When x approaches…

Q: 3 4. lim = 1 1 х-3 ух — 2 — V4 — х 12. х2 — 1, 2 1 5. lim х-з \x — 1

A: Given that: 4. limx→3x-3x-2-4-x=15. limx→31x-1-2x2-1=12

Q: Evaluate the limit sin 2x lim z+0 9x

A: Answer and explanation is given below

Q: ) Find the following limits if they exist. 1 lim x→0 x 1

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Q: Find the limit by interpreting the expression as an appropriate derivative. e2x lim- 1 i X0

A: As we already know that, dydxx=a=limh→0f(a+h)-f(a)h

Q: Compute the limit below. Justify your answer. sin(24x) lim- 39x

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

A: Let the given limit be L - L = limx→0 x2lnsecxUsing L-hospital rule, differentiating numerator and…

Q: Use the table of values and graph to evaluate the following limits a. limx→0 (1-cos5x/6x) b.…

A: limx→01-cos5x6x The graph of y=1-cos5x6x is, From the graph we can see that the value of 1-cos5x6x…

Q: If x Vx sf(x)s -x+ 1for all positive x-values, then what is lim f(x)?

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Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

A: