x +1 1- 3x Evaluate: lim tan -1 tanh |

Q: x + 1 Evaluate lim xS0 1 - cos x

A: We will find the limit by substitution

Q: x tan 2x-2x tan x lim- x→0 (1cos 2x)

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Q: e-(1+x)+/x Evaluate lim tanr

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Q: I- Evaluate the a-Lim(x/(x-1) – 1/ Ix) b- lim [In(cos(x))]* x->1+ x >0 x->0

A: Solution a: Given limx→1+xx-1-1lnx We can write it as…

Q: Find the one-sided limit

A: limx→12-x secπ x Now secπ x tends to ∞ as x tends to 12 from the left side.

Q: lim r-1 X→0 1, 1 + x+1

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Q: tan(4 x) lim x>0

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Q: sin x 3. lim х-30 1 — соSX

A: L Hospital rule

Q: lim cos x+4e* is 5er

A:

Q: lim x to 0 ((1/x)-(1*x(x+1)^-1/2))

A:

Q: lim tan? x-x² 30) x 0 x² tan? x .2

A: On apply the limit we get indeterminant (0/0 ) form so using L'Hospital rule,

Q: Q1: limx→n tan(x) is X-T

A: The given function is tanxx-π. Evaluate the limit as follows. limx→πtanxx-π=tanππ-π=00 Since 0/0 is…

Q: tan x lim x→(T/2)- 2.

A:

Q: 3. A function f(x) satisfies the inequality 1-<f(x) < 1 + tan² x, when x →0. Using the Sandwich…

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Q: x+1 lim V3- х - 2 Evaluate x→-1

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Q: lim -1 x+1 tan t sec 2t lim 3t

A: We know limx→0tan xx = 1 limx→af(x)·g(x) = limx→af(x) · limx→ag(x)

Q: の lim 3x? メ→ 1-cos (x) b) lim 6) Xうo

A:

Q: tan- 2 Evaluate the following: limy- o(2 – x)

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Q: tan2x 4) lim, -X, 2 x- 2

A: Explanation of the answer is as follows

Q: (a) lim 1-cos() 3x (b) lim xe 1/x (Hint: xe

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Q: x + 3x - 4 ? 1. What is lim 2 x→2 2. What is lim tan(x)? 3

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Q: Q1: limx-→n tan(x) is X-T 1

A: Given, limx→ πtanxx-π

Q: lim tan?x-x? tanx-x 30) x 0 x² tan x 2. 2.

A: Evaluate: limx→0tan2x-x2x2tan2x

Q: tan (x – 2) sin(r – 2)4 Evaluate: lim -

A: we want to find the value of limit   limx→2tan2(x-2)sin(x-2)4

Q: lim cos x→1 х — 1

A: Given, limx→1cos x2-1x-1

Q: x+2, x# 1 Evaluate: lim 10 , x=1 00 does not exist 10

A: Topic:- limit

Q: 1. 2. 3. () ) lim lim 2 tan lim (x²–16) x+2 - x →4 4-x х -3 х-2

A: Note : According to our answering guidelines we have to solve only 3 sub parts (if multiple subparts…

Q: 1) lim X-2 2x-4n x(1-cosx) 2) lim х-0 tan(tan?x)

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Q: 1 c) lim x+0 \ex-1 X.

A: the given expression is: limx→01ex-1-1x…

Q: e2x –1- 2x lim -0 1- cos 3x (ii) Evaluate

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Q: tan3x 6. lim X-0 tan4x

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

Q: lim -7 tan x X→(11r/2)

A: solution given below

Q: lim (1+ tan 3x)*

A:

Q: tan 3x Find lim x0 tan 2x

A: We have to evaluate the following limit: limx→0tan3xtan2x

Q: cos2x - 1 Evaluate lim x +0 ex – x - 1

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Q: evaluate the limit.

A: Given:

Q: tan3x lim 20 In(1+ x)

A: limx→ 0tan3xln1+xApplying L'Hopital rule=limx→ 0sec23x· 311+xPut x=0=sec23· 0· 311+0=3

Q: cos x b) Evaluate the limits: (i) lim x→ 0 \2x 4 1 (ii) lim[ x- 2'x2-4 х-2-

A: The objective is to evaluate the limit.

Q: 2) lim (x – 1)tan- 2

A:

Q: B. lim (tan x)* 1-0+

A: Given:  Let y=limx→0+ tan xx2 To Find: To evaluate the given limit.

Q: [3sin(θ)*cos(θ) - θ]/ [tan(θ) - θ]   lim θ -&gt; 0

A: Let  f (θ) = [3sin(θ)*cos(θ) – θ] / [tan(θ) – θ].Find the limit of the function as θ approaches 0.

Q: Find each limit, if it exists.

A: Evaluate: 1. limx→∞ x2+2x3-12limx→∞ x2+2x2-13. limx→∞ x2+2x-1

Q: -1 X +1 M Evaluate : limx{tan X+4 4

A: We have to find

Q: csch(1-2) Evaluate: lim (1 – cos¬' x) x→1-

A: note : As per our company guidelines we are supposed to answer ?️only one complete question. Kindly…

Q: tan(4x) lim x-→0 tan(5x)

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Q: tan³x 3. Evaluate lim x→0 cosx-1

A: While finding the limit of any function, suppose that we have one of the following cases, where a…

Q: lim =cos メ→! X-1

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Q: Find the limits

A: We have to find the limit: limx→0x2-12-cos x Since this is determinate limit so we just have to put…

Q: 12 sin( In x) (b) Evaluate lim,→1 3+5)(x-1)

A: