sin x lim In(x* + 1) x + o+ O 4 O +00

Q: lim (1-e X-

A: Limiting value of function is the value achieved by function when variable tends to approach certain…

Q: Lim x->infinity (cos 1/x2)x^2

A: To evaluate the below limit

Q: lim 1- cos () X00

A: Given, limx→∞1-cos1x To Find the value of this limit function.

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: evaluate the limit.

A: Given:

Q: 1-cos' (x) lim

A:

Q: lim x- Vx x-0

A:

Q: Evaluate the limit.

A:

Q: lim x++∞ x² + x e²x + In x

A: To Find: limx→∞x2+xe2x+lnx

Q: ((주)' lim x (1- cos () COs X->- 00

A:

Q: Evaluode Lim [x]+[2x ]+ n2

A: We know that, x-1<x≤x Therefore, 2x-1<2x≤2x ⇒3x-1<3x≤3x . . . ⇒nx-1<nx≤nx ∴ (x + 2x + 3x…

Q: 1 (ii) lim z-»b b - x

A: The given limit is limx→b-1b-x

Q: lim a-1 In(1-x) dx X

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: 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: 13) lim (n z 2-70 24) lim e- é- ース x - sinx 34) lim (Csx - Cotx)

A: Wherever applicable we used L'Hopital rule

Q: lim In (xth)-Incn) X-DO

A: Topic = Limits

Q: Lim e-ex TEX

A:

Q: lim X→+ 2 In x² 3 In (x+4) ³

A: This question is based on limits solved using L hospitals rule.

Q: Can you help me see how this problem is equal to ln3! Ty!

A: Given limit, limx→∞1x+41x ln3

Q: lim (4 + (x + y} ) In(x² + y)) (х.у) - (0,0)

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: lim 1- cos ( X00

A:

Q: sin (x – 4) x < 4 Let F (x) cos (x – 4) 4< x Find lim F (x). x4+ lim F (x) = x→4+ %3D

A:

Q: lim sin (–3 x z) = z-3

A: To find- the limit.

Q: sin(3 – x) lim x→1 x2 – 5x + 6

A: Explained below

Q: 2sin x lim -0 e - 1 lim - 5 cos x o e - x - 1 4 - 4e* lim -0 xe

A: As per our guidelines, we are allowed to answer the first question only please resubmit the other…

Q: lim 1-e*) X-0 x sin x

A:

Q: lim COos x –1 x→0 x² – x³

A: To evaluate the given limit.limx→0 cos x-1x2-x3

Q: Lim 87% x- 4 tos x 2 x

A:

Q: 2 lim キx°- キx - しx* -I 3 x メ→ o -\x3+ キメ - 12

A:

Q: sin x 4. lim x0 et In x 6. lim

A:

Q: a lim 6. *a Jx- Ja -x

A:

Q: lim (sec³ x – tan n³ x)

A: We have to evaluate the given limit: limx→π2sec3 x-tan3 x We know the identities, sec x=1cos xtan…

Q: メ e- (X+\) メー→o CoSX -1 lim

A:

Q: lim Jx-S

A:

Q: lim ecos x = x→0

A:

Q: 2 sin(z) – sin(2z) lim -10 z- sin(z)

A: We use L'Hospital rule to solve this limit problem.

Q: lim x (1 – cos X→-0

A: limx→-∞x1-cos1x

Q: lim (2,1) (0,0) (1 + (x² + y²) In(2² + y²))

A:

Q: sin(3 – x) lim x→3 x² - 5x + 6

A:

Q: lim (1,4) (0,0) x2 + y2 Prove that

A:

Q: lim cos(x) X- +x 3 TC 2.

A:

Q: arctan(x2) lim x8 lim a In(x) = X→0+

A:

Q: lim (2 + (x + y²) In(x² + y³)) y)→(0,0)

A: Here, lim(x,y)→(0,0)2+x2+y2lnx2+y2

Q: sin 2x lim x→0 5x2 + 7x is 2 А. 7 В. О C. no limit D. undefined Е.

A:

Q: tan(x)-sin(x) e. lim x2 tan(x) (In (cos(3x))] f. lim 2x2 tan(x)-x g. lim x0 (sin(x)-x. ex-In(1+x)-1…

A: e) Given data:   The expression for the given limit is limx→0tan(x)-sin(x)x2tan(x).     The given…

Q: lim lx-1| х>1 1-х ?

A:

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

A: