2r-1 ifr<-I "(x) = x²-1 if – 15x52 · evaluate lim x+2 ifx>2

Q: 1-cos(x) Find lim x-0 2x

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Q: Limx-->9 = X -9/ (X)1/2 -3

A: We will first cancel out the irrational factor at the denominator. And then we will check if the…

Q: 2. Find if possible: sin(nx) a) lim x-4 x2-16 b) lim x (sinx+(cosx)³) (x2+1)(x-3) c) lim,--o (cosx)

A: a) Given that limx→-4sin(πx)x2-16we have to find the limit of…

Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: 1. limx→4 4x-x² 2-√√x t²+3t+2 2. limt-1 2-t-2

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Q: 9x +1 lim x - 1 V1+x-1 lim x-0 lim 2x2 + 3x lim x05x2 - 2x Dr ohammed Jas

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Q: lim х>1 \x-1 X→1 Inx,

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Q: lim x approaches 2 .............. 2x + 5/[11 - x^3]

A: here we have to find the limit.  A=limx→22x+511-x3

Q: 2х + x 1. lim

A: Consider the limit  limx→02x+xx

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: 1. lim(2x – 5) x+4 2. lim(3x + 8) x-1 3. lim *+1 X-2 x-5

A: Disclaimer: Since you have posted multiple question, we will be solving first three. In case you…

Q: 8x+4-4cos?x+tanx Q1) Find lim x-0 4sin2x

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Q: 2 1 lim х->1| х — 1 X→1 X - 1

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Q: 2Tan 'x -x 9. lim, 2x – Sin^x

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Q: 1 lim x→11-x .3 —х 1-х*

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

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Q: 1. lim→- Зx? (2х - 1) 1 + 4x + 3 9. limx--3 x2- 3 2.

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Q: 4 - VE lim x>16 16x – x?

A: Given: limx→164-x16x-x2

Q: lim as x--> 0 of (1-2x)^1/x

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Q: 4 – x lim x - 4 5- Vx² + 9

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Q: x2-4 1) lim x-2 x-2 sin 2x 2) lim 1 1 3) lim(-- X-0 x VX

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Q: 5. Evaluate lim sin(x)– (x² + 3x – e*). (x³ – 2x2 - 6 + 3x) 6. Evaluate lim X→2 х - 2

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Q: 3 x' tan (x) lim - 3 4x* + 2х-1

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Q: d- lim x+1 /V2x²+x+1

A: First take x common and then use l hospital's rule to find the answer.

Q: xtan x Solve for the lim X0 sin 3x

A: Given : limx→0x tanxsin3x   To find : Solution of the given limit?

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: (1 – V3x lim tan- 3 + x x-00

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Q: limx->0+ (x^(e) -5x^(4) -3x^(6) - x^(3) +100)

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Q: x2-3x-4 3. lim x---1 x+1 1- -5 2- zero 2- 4- -3

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Q: Inx lim X+o x3 lim- x-0 ex - x2 - 1 lim- 0 sin'3x

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Q: Evaluate

A: The limit of a function at a point is the value the function tends to as x tends to that point. For…

Q: cos x-2sinx 1. limx-n 3cosx -2 limx-3 X-3 3x6-x*+2x-3 limy--o 4x5+2x3-5 iv. lim,→-1(x³ limy--1(x³ –…

A: [i]

Q: 2. lim x sec 2x

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Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

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Q: 1) lim-sinxr x-0

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

Q: 2- x - sinx 1. lim x00 x + cosx x*+2x-1 2. lim-0 x3-2x2+x

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Q: d: (a) lim ズー2 オー2--(*+1)

A: Answer:  The solution is as shown below:

Q: Find the limit

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Q: (2-4* limx-1 sin(x³–1) X. x-1

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Q: find lim x-> 0, cos (12x)-1 / 3x

A: Given,              limx→0cos 12x - 13x Move the term 1/3 outside of the limit because it is…

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

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Q: 2Tan 'x - x 9. lim,0 'x0 2x – Sin 'x

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Q: x3–1 х-14x3-х-3 1) lim sin 2x 2) lim x→0 2x²+x 3) lim 1-v х-1 1-х

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Q: 3 lim tan³ 2x x→0

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Q: 1 1 i] lim 2 1--3 x-2 ii] lim- x-* 2x-6

A: Apply put the limit and solve it

Q: 25+x-5 4-limx-0

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Q: cos 3x – cos 2x - Evaluate limx→0 x2

A: Consider the given function, limx→0cos3x-cos2xx2 applying the limit to the function we get,…

Q: 2tan x- x lim, -1 2х -sin " x,

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Q: 2х а) lim -1-2x (sin 2x)+² - et b) lim -4x - cos x

A: