sin 3x 1. Find lim x→0 sin 4x

Q: 1 + x + sin x 47. lim 3 cos x 49. lim Vx + 4 cos (x + T)

A:

Q: 5. x sin 3) lim00 x+1

A: limx→∞x5sin5xx4+1=limx→∞ x5sin5xx41+1x4= limx→∞ x sin5x1+1x4 = limx→∞  sin5x1x1+1x4=limx→∞ 5…

Q: 2. f(x) = sin(x) lim sin(x) - et x + 00

A: Calculate the limit and horizontal asymptote in the following way: (2).              f(x) = e-xsinx…

Q: lim sin(x)d.x (x2 + e2)2

A:

Q: sin ( T cos? x lim- TT COS X X' 2.

A:

Q: x sin 4x b. lim x-0 1-cos3x

A:

Q: Rx+2sinx Q2.a) lim sin (). sec (in 3+x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2 xt (* sin) lim sec x lim X→+0 X. 2

A: Given limits are  1) limx→∞xsin2x2)limx→π2secx3)limx→0sinxx

Q: x sin(3x) lim x→0 sin(x2)

A:

Q: エ→2 x² -4 1- cos 2x 7) lim X sin x エ→0

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Q 3/ x-sin x A- Find lim,0 1-cos x.

A: Explanation and solutions is given below....

Q: x sin(x-1) с) lim х+1 2х2-х-1

A: Solution: The objective is to find the limit value of the given function

Q: et sin x — х - lim x → 0 5 cos x – 5 ||

A:

Q: (b) lim ln(sin x) x→0+

A: b) limx→0+ln(sin x)

Q: tan( xy) lim (х.у) >(0.1) х"у+x = ? 1 (b) 2 1 (c) 3 (a) 0 (e) 1

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: 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: e-3sin z (c) lim x² (d) lim sin(rx) lIn (x – 1) x→1+

A: The given limit is: (c) limx→∞e-3sinxx2  To find the value of the limit.

Q: x 2 sinx Q1//A- f(x) = x <= COSX Required: lim f(x) 4

A:

Q: Find the limits

A: Find the limit limx→-πx+4cosx+π

Q: x + sin 2x lim x-2 x – sin 2x О з O 2 O 1/3 О 12 O other:

A:

Q: 4x(1 — сos(x)) lim х — sin(x) х>0

A: Because the limit is in 0/0 form. Apply L'hopital's rule.

Q: (d) lim (e) lim (1 – sin(x))/-

A:

Q: 2 sin x 1 lim is

A:

Q: sin(9x) (d) lim x – 7 (e) lim 7| (f) lim x8, COS

A: We have to evaluate the following limits

Q: 1 + sin xT - lim X0 1+ cos x

A: We have to find the limit.

Q: 2x tan x+ cos I COS T lim

A:

Q: Rewrite the following as one-sided limits as in Exercise 50 and evaluate.

A: To evaluate the limit. (a).…

Q: 2) lim sin 4x

A:

Q: Lind Lim Sin'(Ox) sin (sx) X-o

A: According to the L'Hospital's rule, if limx→mf(x)g(x) takes the form of 00 or ∞∞, then limx→m…

Q: sin(2rx) lim x → 7 x2 – 49 -0.2857 T 0.2857 T -0.1429 T 0.1429 T

A:

Q: e* – 1 lim x-0 tan 2x

A: Given: limx→0ex-1tan2x

Q: -2x – 1 Find lim X+0 sin 3 sin()

A: Using formulae of limits

Q: T+tan x 4. lim sin X→0 tan x-2 sec x,

A:

Q: L’Hôpital’s Rule for ∞ /∞ Evaluate the following limits.

A: Part (a): Given, limx→∞4x3-6x2+12x3-10x+3

Q: 1.) lim 2x sin'x. *P0 ex - x - 1

A: We apply l- hospital rules and solve it. Follow 2nd step.

Q: t x sin(t + 1) lim --1 t +1

A: Given : limt→-1t×sint+1t+1

Q: 4 lim sin(x) х>0 х 41

A: Given that

Q: sec2x-2taпх lim X→T/4 1+cos4x

A: Consider the given limit limx→π4sec2x-2tan x1+cos4x   limx→π4sec2x-2tan x1+cos4x=00 Which is…

Q: 4. Evaluate if they exist: (a) sinh x dx (b) lim , sinh x dx r+00

A:

Q: 5 sin(6x) lim x→0 3x

A:

Q: х(4+sin 6x) 3. lim X→+0 х+1

A:

Q: 4+ sin x d. lim - 1- i cos(x+x) +2 g. lim

A: To find out the limit, substitute 0 for x and find out the limit value

Q: 9) If y = sin(sinæ), then y' is: x + 2| lim (x +3) I→-2- x + 2

A: See the attachment

Q: Find the limit.

A: Our Aim is to evaluate limx→∞ x sin 1x -(i)

Q: 3x+1 lim 1 sin x)

A: Given,         limx→03x+1x-1sinx

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.