10. lim ) 1 -1) A-0 hV1+h sin x 13. lim 0 2x-xr V8+x -2 (Hі 16. lim

Q: Calculate each of the limits in Exercises

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

Q: 1- cos(2x) lim x→0 х-0 1 — сos(6х) 7* – 6* – 1 lim x→1 х2 — 1

A:

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

A:

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: Compute Lim メーフ4 7x+5 -3 Sin ? X 2)x-70 3X イメ2+2 3) -00 X-7-00 2x-1

A: (1)Consider the given function with limit:

Q: Can you solve number 23

A: The given expression:

Q: Finding Limits #23 please

A: Given information:

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: why is limx->0[x^4 * cos(2/3x)] not equal to zero? I thought that if I plug in zero to x^4 it makes…

A: Given that: limx→0x4.cos23x

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: Prove that 2" + 2* -6 lim tan'x - 3tanx lim 2* -2 1-/3 cos (x+ p/ 6)

A:

Q: 2 сos(6x) — 6 2? — 2 os(6x) – 6 x² sin(5x) – x2 – 5x - | lim x → 0 - -

A: We have to calculate the given limit: limx→02cos6x-6x2-2sin5x-x2-5x

Q: .2.4 lim (z,y)→(0,0) x² + y?

A: follow next step

Q: ズ→27 7. lim v3x2 – 2x + 8 ズ→2 8. lim vx (2x) ズ→20 x+5 9. lim -15 V 2

A: Given query is to find indicated limits.

Q: c) Without using L'Hopital's rule find х3+7x2-14х+6 lim х>1 х5—х4+8х3-8х2+16х-16

A:

Q: 9. - (a) Compute lim I--3 I-3 sin (0) 0 0 2 cos2 (0) -2 (b) Compute lim 1 (c) Compute lim I-0 I -

A: a. limx→3x2-9x-3limx→3x+3x-3x-3  x≠3 ,a2+b2=a+ba-blimx→3x+3=6b. limθ→0sin2θ2cos2θ-2Using L hospital…

Q: By L'Hopital's Rule, X-2 lim x→2 X²-1 1 1 lim. = x→2 2X 4

A: L’Hospital’s Rule: Suppose that  limx→a f(x)g(x)=00  OR  limx→a f(x)g(x)=±∞±∞ where a can be any…

Q: H-w in limits 3-3- 2.21 9 iaam ) Lim. 1- CosC2K) Sin (24) 2 - メャ3 2) Lim x2x -3 3) Lim (X+4}-16

A:

Q: 6xsec 3x 2-If y = (tan3x)" prove that = (tan3x)²"| + 2ln(tan3x) %3D %3! tan3x

A:

Q: Find f(a)  a=2

A: We know that the definition of derivative is: We write the given equation in this format and find…

Q: Theory and Examples

A: limx→02x23-3cos x

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: 2. -1- -729630 -540 --450 –-360 270 -130 -90 90 130 270 360 450 5 40 6 -1- --2 -3- -5- y = 3 sin(x +…

A: The mid-line is the point of reference. So to find the mid line we have to find the average between…

Q: lim (x,y)→(0,0) x3y is equal to----- x6+ y2 (a)1 (c)does not exist (d)-2

A: In the above problem, at the point (0,0) the function is not continuous. So, it is not possible to…

Q: 10. a.) Use: lim 2(x, )ar = [ Ax)dx , i-1 b- a Ax = and x, = a +i Ax %3D %3D to evaluate (5x² – 2x³…

A:

Q: 4х —Зx2+2х-1 Solution of lim is .... хэ0о 5x3+14x2—7х+2 4x5—3х2+2х-1 Nilai dari lim adalah .... х>0о…

A: The given limit is: limx→∞4x5-3x2+2x-15x3+14x2-7x+2

Q: 7) Show that lim = 1. 200 (z-i)3

A:

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: 2-limyo(x.secx.cscx)

A:

Q: What is the lim (3)¯ I 7 sec (7x) cos(3x)?

A:

Q: 16+y limy-o

A: The given function is 16+yy-4y. Simplify the given function as follows.…

Q: 2. Show that lim (x,y)→(−1,0) (x + 1)² sin y (x + 1)4 + y² does not exist.

A:

Q: 3 a. lim うルーフ4 4- 1し 5- J3c+9 2-Jつい 5. しim うしー72 ル+2-Vt4んt4 C. Lim 2021+リ-26 ルーフ 20t ーて

A:

Q: 2,,2 x²y² lim (x.y)→(0,0) x4 + 3y4

A:

Q: 1 4. lim 2t-1 t-

A: Note:- We will answer the 4th question since we answer only one question at a time. Please submit a…

Q: 4 - V5t + 1 lim +3 vt +1– 2

A: Let L=limt→34-5t+1t+1-2

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

A:

Q: 2 tan (3x²) 1- _ 2 tan c∞) 2 teanCo lím %3D メ→の 7x2 の -> 6X Ifm a tan (3x) lim 2-1 +3x) x70 x 70 14x…

A:

Q: 1. lim ux-121 X-3

A:

Q: Show that lim (x,y) → (0,0) 12 √16x +9y¹ 4x²+3y does not exist. Please show a complete solution.

A:

Q: 3z+ 4y lim (2,0) +(0,0) 2z - 5y OA- OB OCo O D. Does not exist

A: Explained below

Q: 13x3sin(는)= 13 2.플) .3, lim %3D (x.y) → (1,-

A:

Q: 3. Prove lim 3x-7= 2 X-3

A:

Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

A:

Q: If f(x) = xcosx then limf(x+h)-f(x) h COSX = ? %3D %3D h-0

A:

Q: riemann from 0 to 2 of 2x+1

A:

Q: Q show that lim %3D メ→ 0-1

A: We have to show that limx→0.11x=10 L.H.S : limx→0.11x           =10.1               (plug in the…