Q1/ (a) By using the definition of limit, prove that lim (3x+iy)=9i. z31

Q: Calculate the limit algebraically. If the limit does not exist, say why. lim(x + 1) O -1 does not…

A: This is not always feasible, but there are some cases that work. If f(x) is a polynomial function,…

Q: Evaluate the limit, using L 'Hopital 's Rule where it applies.

A: To evaluate the limit using L-hospital Rule. limx→9x12+x-6x32-27 Solution: It is 00 form. We know…

Q: 4) Find the value of a for which the limit lim x→0 evaluate the limit. sin(ax)-sinx-x x3 is finite…

A: To Find: The value of a for which the limit limx→0sin(ax)-sin(x)-xx3 is finite and then evaluate the…

Q: estimate the limit numerically to two decimal places or state that the limit does not exist

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Q: Evaluate the limit with either L'Hôpital's rule or previously learned methods. 5t In(t) lim t- o 8 +…

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Q: Find the limit, if it exists.

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Q: Vx2 – 9 4. lim х-з х — 3 X→3

A: Given limx→3x2-9x-3

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: Here it is required to estimate the limit numerically to two decimal places.

Q: Let Sz+8 3x +8 I-1 Approximate lim f(z) numerically and verify your answer graphically. If it does…

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Q: Evaluate the limit: lim z-10 sin (4z)

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Q: Find the limit for the following function by using L'Hopital's rule: tan-1x-tan-11 lim x-1 x2 – 1

A: limx→1tan-1x-tan-11x2-1

Q: How do you evaluate the limit:  limx-->0  (sin(4x))/9x WITHOUT using L'Hospital's Rule?

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: limf(x) does not care what happens While a limit exactly at x = c because the limit is concerned…

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Q: Use different path of approach to the point (0, 0) to show that the limit lim(,9)→(0,0) 4 does not…

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Q: Evaluate the limit: sinx lim x→0 e4x – 1

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Q: Find the limit.

A: Given- x→lim0 sin3xx To find- the value of the above limit. Formula used- Using the standard form as…

Q: X- Zx +3x+2 lim

A: Solution of question as follows

Q: lim ("V52"-1

A: Given: limn→∞52n-12n   We know that the radical rule; amn=amn

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

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Q: Use the e-8 definition of a limit at infinity to prove that lim = 0. %3D

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Q: Determine the infinite limit. limit as x approaches 3 from the right side of ln(x2-9)

A: We have ln(x2 - 9 ) if we take x as √10 which is approximately equal to 3.16, then, x2 - 9 =1…

Q: x² - y? lim ) - (0, 0) х? + у? y

A: Here we have to show that, lim(x,y)→(0,0) x2-y2x2+y2

Q: 4) Determine the limit. lim 1 f(x), where f(x): X + 10 X-- 10-

A: Given, f(x)= 1/(x+10)

Q: Prove that lim 4x – 2 = 10 using the epsilon-delta definition of a limit.

A: Let, ε>0 is any number. and δ>0 is also a number. For the given limit, fx=4x-2a=3L=10 From ε-δ…

Q: Estimate the limit numerically or state that the limit doES not exist (DNE): sin(9r) lim

A: Evaluate: limx→0 sin9xx

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim- X0 sin 2x -16 2. lim X-4 (Vx+5)-3

A:

Q: 9 -x2 if x 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using…

A: For a function to be continuos, the left hand limit should be equal to the right hand limit.…

Q: Prove the limit. Using the precise definition of a limit. lim x approaches 0 xsinx(1/x)=0

A: To prove:

Q: Find the limit. limx 0 √(x2 + 4)

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Q: 1b. Use L'Hopital's Rule to find the Limit:    lim      2tanx/sec2x x->pi/2

A: To find the limit

Q: 2. Find the limit using Squeeze theorem 1 lim-2|x – 2| sin( r - 2

A: Squeeze Theorem- Let f, g and h be functions defined on an interval I. Let c∈I be its limit point.…

Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(12r) lim

A:

Q: How do you evaluate the limit:  limx-->0 (1-cos(7t))/(sin(7t))   WITHOUT using L'Hospital's rule?

A: Since the given function is function of  variable t but in question limit is given for variable x.…

Q: Find the limit. lim e^(-2x) x-->∞

A: To find the limit of e^(-2x) as x tends to infinity.Check whether the L Hopital’s rule applies.

Q: . Suppose f(т/3) — 5, f (т/3) — —3,а sin(3та) 2->0 sin(5Tx) . Find the limit: lim

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Q: 1e. Use L'Hopital's Rule to find the Limit: lim (1+4x)3/pi x->0

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: 5) Find the indicated limit if it exist. 3- Vx + 7 а) lim x→2 2 - x x' +1 b) lim х>-1 х+1

A: (a).    We have to find the limit: limx→2 3-x+72-x

Q: Estimate the value of the limit lim, 40 COS x if it exists, by filling out this table and then…

A: We have to find the limit of the function and want to find some values to conclude graphically.

Q: 2. Use e -d of the limit to prove that lim z= 4

A: Given below the detailed solution

Q: 1f. Use L'Hopital's Rule to find the Limit: lim (tanx)x x->0+

A: Given,

Q: Q1:Find the limit using L Hopital rule In (csc x) lim xT/2 (x – (1/2))²

A: Given limx→π2ln(cscx)(x-π/2)2 We have to find limit by using L Hospital rule L'Hospital's Rule…

Q: Find the limit: limx→0​ x3sin(1/3x​3)

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Q: Q5) Find the limit for the following function by using L'Hopital's rule: tanx - tan-11 lim X-1 x2 -…

A: We find limit

Q: Verify using the definition of limit (with e and 8) that lim 1|+3) = 3, x1 xplain all the steps and…

A: To verify the below limit using the epsilon-delta definition. limx→112x−1+3=3

Q: 8. Find the limit using squeeze theorm. lim x² sin(x²)

A: