1– tan(*,) [1– sin x] lim 1+ tan(x (¥2) [z – 2x] x- - 2 1/8 1/32

Q: 5. Evaluate lim sin(x)-(x² +3x– e*). 1-0

A:

Q: Q:Prove that: Vi+x+x² -1. Lim- 12-2 cos x + lim x->T/4 sin(x - T /4) > log, 0.005

A:

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

A:

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: 1-cos x 9. lim x00 x2

A:

Q: (12 sin )( In x) (x3+5)(x-1) Evaluate limx→1

A: Here we have to evaluate the given limit .

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

A: The solution are next step

Q: 1 2. lim cOs X -

A: The given function rewrite as

Q: cos x ln(x - *) *-+ In (e-e*) 6. lim

A: Topic:- limits calculus

Q: -lim COS X tanx <-2メ X-8 2 lim 3 x→2 x42x +X-2 A

A:

Q: 111. lim cos x -2

A: To find,

Q: b. lim cos(x)-1 x2

A:

Q: COs x lim 1 (b) In(2/9) – In(x(1 – x)) x – 2/3 - - lim x→2/3 (c) lim r(tan x2 - In x lim x0+ x In(1+…

A:

Q: 2 In (1+ lim X -00 3 tan 2 x

A:

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

A:

Q: find 49. lim 0 - sin 0 cos e tan 0 - 0 sin 3x - 3x + x² 50. lim sin x sin 2r

A:

Q: 1) lim (tan x) cos x X-2

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: 44. lim sin² x x→n/4

A:

Q: x-sin x' A- Find limx-0 1-cos x.

A: We will apply the L'hospitals rule because the limit is of 0/0 form.

Q: i) lim(In (3x– 2)– In(5x+4)) Зх +1 lim 1 j) x0* sin x k) lim (csc x- cot x + cos x)

A:

Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: (c) (d) sin 3x lim z0 tan 3r lim (In(sin 2x) - In(tanz)) +0+z

A: Here we have to solve the given limits.

Q: 1 + cos(x) a) lim %3D 20 -x ) lim x-1( In(61x-60)

A: Given, limx-&gt;π (1+ cos (x))/(6(x-π)²) = (1/6)limx-&gt;π (1+ cos (x))/((x-π)²) = (1/6)limx-&gt;π…

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim X x→0+

A: Solution: a) limx→0+sin xx1x2

Q: x 0+ (d) lim (1 – 2x)¯4" -4x x→0+ (e) lim (sin æ)-In æ (f) lim (– In æ)*in æ sin x

A:

Q: (1) lim,o In (sec x) 3x (2) lim, (tan x)*

A:

Q: (1) lim (In ) = z (x1 (j) lim rsin z x→0+ sin 2x + 2 arctan 3x + 3x2 (k) lim x→0 In (1+3x + sin? x)…

A:

Q: 3. Find lim x sin II

A: Given limx→∞xsin(πx)

Q: 1-cos (xーT) lim X-n (x-)sin (x-n)

A:

Q: 5. Evaluate: lim, 0 2x- x2 sin a 1 Does not exist 2.

A: lim (2x-x2)/sinxx→0

Q: . Does knowing that | sin (1/x)| < 1 tell you anything about lim (x,y)→(0,0) y sin -?

A: To find the limit of the problem

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: (a) lim x→0+ (sina) 1 (b)…

A: Given: (a) limx→0+sin xx1x2            (b) limx→01sin2 x-1x2 To find: Evaluate using L'Hospital…

Q: 1-cos*x 5. lim X-0 xsinx

A: Given,

Q: 4-V16+h 9. lim x+sin x 12. lim

A: Note: As per bartleby guidelines for more than one questions asked only one question is to be…

Q: 30. Use the fact that lim x→0 sin x X = 1 (shown in video) to show lim x-0 1 - cos x X = 0

A: we will find the required.

Q: 7- sin-(e*) 2 lim V1 - e2x

A:

Q: (2-4* limx-1 sin(x³–1) X. x-1

A:

Q: 1+3x COS x - 2.) lim tan x

A:

Q: 1 Evaluate: lim (1+2 sinh x)+20 x→+∞

A:

Q: 1-cos (x-T) lim x→T(x-T)sin (x-π)

A: Given limit, limx→π1-cosx-πx-πsinx-π

Q: lim -Vx + e* + sin(x)cos(x) 1+ In (x)

A: limx→3-x5+ex1+ln(x)+sin(x)cos(x)=-35+e31+ln(3)+sin(3)cos(3)

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x x→0+

A: We have to determine limit by useing l hospital rule

Q: 8 sin((k – 1)x) sin (2x) П ¤(ekz – 1) lim \k=2

A:

Q: ¶/x x-0 sin (1 /x) Lim

A: To evaluate: limx→∞π/xsin(π/x)

Q: 73. lim In(cos x)

A:

Q: 2x e* –1 lim- x→0 sin (2x)

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