2x° – 3x"–21 Il -21 lim 13x-4x°+2x

Q: (2-4)* Q1: limx-1 sin(x³–1) x-1

A:

Q: 1 (a) lim 2x+sin x 5x+2 (b) lim 1 (c) lim cos -

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2 cos(4x) – 4x2 – 2 lim - I→0 sin(2x)- x2 - 2x

A: We have to evaluate the limit limx→0 2 cos(4x) - 4x2 - 2sin(2x) - x2 - 2x

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

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Q: a. limr→0 cos(x) b. limx→n

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Q: ) lim- 1 5 arctan -4arctan |=? Use L'Hospital's Rule 4 X-0 xVx

A: L'Hospital's Rule tells us that for calculating limit of a function if we have an indeterminate form…

Q: 2x - 6x 34. lim x-0 sin 2x 35. lim 2 1- cos 2

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Q: lim, →2, 1 X – 2J2x

A: The limit of the function is given limx→21x-2∫2xx2dt1+t3. To check the limit of the function ,…

Q: 2i(2-i) lim z² + 1 - 1 2i 1

A: Solution: Given limz→i2iz-iz2+1 We have to find this limit.

Q: 3z2-12z + 13 5. lim zI 4-16z+5z2

A:

Q: cos(²²) – 1 ()- lim 7 x3

A: Given that, limx→0cos(x2)-17x3 By using limx→0cf(x)=climx→0f(x), where c is constant.…

Q: 5] y=1+2x6 – 4x² – 2x6 - Standard Form: Degree: Sign of LC: as x→-0, y→ as x0, y→.

A: Solve the following

Q: I+3 lim z-3 + x- 6

A:

Q: {) Lim 1-cos Scos2x 7 メー)○ x2

A: Given: limx→01-cosxcos2xx2 for evaluating given limit, we use L hospital's rule according to L…

Q: lim x-0 (cos20x) 7/20x^2

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

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

Q: 16. lim (2 – 3x) = –4 x → 2 %3D - 19. lim (1-3-) -- 3 20. lim 2 = 7 x → 5 21. lim x2 – 2x – 8 = 6 x…

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Q: 4) lim1+ 1 = ? %3D - r-

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Q: z? +1 lim z4-1 %3D i O -i o

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Q: lim (3x + 1) sin(2x) 4x2

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Q: 1) limy-o 2ytan(1/y) sin(r-0²) 2) lim2n 101-Va 2 3) limg-n/2 (n²-482 )sec\ß] tan2x 4) lim T

A:

Q: 2 i (z-i) lim z?+1 1 -1 о 2i

A: 1 Just use L'Hospitals rule.

Q: ()- (T I-1 lim 2x-1 |47–1

A: We have to solve

Q: 1 limx-0- (x 8 %3D x2

A:

Q: (а) 1- cos 4x lim x? x-0 5-х (b) lim- 45 Vx-1-/2x-6 312 -t- 2 lim 1² -1 (с)

A:

Q: lim (4+ (2? + y°) In(x² + y²)) (1,y)(0,0)

A: Given; lim(x,y)=(0,0)[4+(x2+y2)ln(x2+y2)]

Q: ピ+5 1 lim t一+0|5t2 +6'2t (?, ?)

A:

Q: 4x +4 lim (2,y) (-1,2)` x² + 3xy – 3y2 + 3xy - 3y2

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Q: -2ln(cosx lim, 0 ,2

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Q: lim a sin(1/2),

A: Given,           limx→0xsin1x

Q: Example 48 lim,→∞(Vx² +x – Væ² + 5) =?

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Q: 2n -1 (i) lim = 2

A:

Q: ..... ..... If a and b are constants and lim asin(4x)-btan(8x) 3, x → 0 4xcos x+8sin(12x) then a-2b=

A: Solution is given below:

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: sin(4z) 7. lim I-0

A:

Q: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

Q: Find: lim→1+i z2 –z+1-i i z2-2z+2

A:

Q: 1. Find lim an 3(x+h)-tan 3x A. 3 sec 3x tan 3x B. sec? 3x C. 3 tan 3x D. 3 sec2 3x

A: limh→0 tan3x+h-tan3xh So here fx =tan(3x) Now we need to find derivative of fx with respect to x…

Q: lim 15 13 15z2 Vr? + 8z lim %3D HY8 9-4x Vr? + 8z lim 9-4r /7

A: Given query is to find limit of the expression. Since first three has been filled correctly, solving…

Q: 3 lim tan³ 2x x→0

A:

Q: Q1: limx→1sin(x³–1) x-1

A:

Q: ANS: (d) |z - 3| lim 243- 12 6 - ANS: -

A:

Q: 1 2 1 + lim Р-(-1,2,0) х- 2 у -5 z+4 II

A:

Q: Solve z4-1 lim z→i z-i

A: The given expression is: limz→iz4-1z-i

Q: 2つi 2×+1 Find Lim レ わサズ

A:

Q: I-1 lim I→1+ Vr²–1

A:

Q: lim %3D X2 -マメ

A: The solution for the above question is as shown below.

Q: 19 lim I-3 T+3

A: It is given that, limx→-3+x3+9x+3We have to evaluate it.