(1+x) — е* 20х2 lim

Q: (2-4)* Q1: limx-1 sin(x³–1) x-1

A:

Q: 9. Lim 6x - Sin 2x メ→0 2x +3sin 4X b. lim x²-1 1/2

A:

Q: 42t lim t+0 4 - 1 - 1

A:

Q: Compute x-+xX lim X-700 It Ttx Sinx 2) Lim X-70 CUSX-1 X3-1 1L-X

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

Q: (2) 1: limx-1 sin(x3–1) x-1

A: limx→1 (2-1x)2sin(x3-1)x-1=limx→1 (2x-1x)2sin(x3-1)x-1=limx→1 4x2-4x+1x2sin(x3-1)x-1=limx→1…

Q: lim [r – In(4x + 7)] x→+0

A: To find the limit

Q: sin(4x) 8. Compute lim x-0 tan(3x)

A: The solution are next step

Q: Зx2-14х +8 lim 7x-28 x+4

A: By factoring method: Take factors in numerator and denominator  Limx-4(3x2-14x+8)/(7x-28)         =…

Q: Evaluate limx-->2 (sin(x-2))/(x^2+4x-12) Without L'Hospital's rule.

A: limx-->2 (sin(x-2))/(x^2+4x-12)Numerator = sin(x-2)Denominator = x2 + 4x - 12 = x2 +6x - 2x - 12…

Q: -1 sin (5x) lim

A: The given expression is limx→0sin-15xx the given expression is the indeterminate form 00 Apply L'…

Q: Q3) Find: (1) lim, 1+cos 2x (2) limx→-2- (x + 2) |4-x²| 2-x

A: Q3)1Here, we need to calculate the limit of ,limx→π21+cos2x4x-π2

Q: find: a) Lim x4-1 x2 b). Lim 10x-3 SinX

A: We have to find the following limit      alimx→1x4-1x2-1       blimx→010x-3sinxx

Q: tan (2x) 3. 24. lim- %3D .3

A: We replace tan(2x) by sin(2x)cos(2x)…

Q: ze" – In(1+#) lim

A: To evaluate the given limit.

Q: Show limx→∞ xne−x = 0 for all n = 0, 1, 2, . . . . To get started notice that when x ≥ 0, all the…

A:

Q: lim X(In x)2 requires repeated application of L'Hopital's rule. Show all the steps.

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Q: Find the lim inf (xn) and lim sup (xn) of Xn=3-(-1)"

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Q: 2 2- limx-1 sin(x3-1) x-1

A:

Q: 1-coskx 2. lim = 0. kx

A: We have to find the limit of the function (1-coskx)/kx when x tends to 0 .

Q: Evaluate: 1- cos(x) 3x2 lim Express your answer in 4 decimal places.

A: According to question,Given limit,limx→0 1- cos x3x2

Q: lim (In w-

A:

Q: Find the limit.

A: We can find the limit of an expression by applying the limit point as value of the variable in the…

Q: 8. lim vx +6x+1-Vx² +x

A:

Q: Find lim 1+1? 1-e24 -2t -1 tant, 2 2 1-1

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Q: What is the limit as x goes to infinity of (ln(x3 + 9) - ln(2x3 + 17x))?

A: Use quotient rule of logarithm to reduce the function as shown,

Q: lim x yields to 1  x-1/(square root of 4x +5)-3

A: As the given limit is not legible, the limit is computed in 2 cases. Obtain the limit as follows.

Q: Evaluate limx-->0 (x^2)/(sin^2(7x)) 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: lim (In x)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: lim メ→02-V4+x Calculate

A: We have to find the limit of the given function.

Q: lim x---q x2/2x

A: limx→ qx22xPlug in the value x=q=q22q=q2

Q: (i) Evaluate In (1-z³) lim 2->0 sin (2z

A: We need to evaluate the limit If the value of the function after putting the limit is in the…

Q: 11. lim x→ー4 x2-16 2x2+9x+4 z2-36 12. lim Z--16 Z-6

A: (a) We have the given limit problem as limx→-4x2-162x2+9x+4 On calculating the factors of numerator…

Q: 1) lim-sinxr x-0

A: given equation is     limx-->0  (x-sinx) / x³ ** L hospital rule =>    limx-->0  f(x) /…

Q: lim (In(3x + 1) – In(2x + 1))

A: To evaluate the below limit

Q: Calculate the limit.

A: We have to find the limit: limx→∞ln3x+1-ln2x+1 It is ∞-∞ form. Simplifying further using logarithmic…

Q: Q1) Find lim Bx+4-4cos²x+tanx x-0 4sin2x 10x2+125-5 Q2) Find lim x-0 3x2

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Q: 1 lim 2 -1 x* -1,

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Q: -11x lim I+00 11 + 2x -1 6x – 12 lim 1-00 r3 + 9x – 14 ,2 lim x→0 12 – 15x? V2² + 15x lim 5х — 13…

A:

Q: lim In(10x) x-0t

A: To find the below right-hand limit.

Q: /14-х-3 lim 1-V6-х X→5 4-Vx lim х>16 16-х

A:

Q: lim x in (It -)

A:

Q: 5 15 lim z00 10 x13+26 x15 Number Show your work and explain, in your own words, how you arrived at…

A: L=limx→∞(5x1510x13+26x15)dividing N and D by…

Q: 1 lim In csch (1– 2x,

A: Let L is the value of given Limit

Q: 2tan x- x lim, -1 2х -sin " x,

A:

Q: 1 lim(x²-3x+1) 3. lim tan(x²) 7. lim 2²-1-2 x²-4

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 3-Vx2+9 Without using L'Hopital's rule, find: lim-

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Q: lim as x goes to 0 (sin(2x)+7x2 - 2x / x4 + 2x3 + x2)

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.