lim 2x'e X- | X→+∞

Q: lim (1-cos x1/2) / ln(1+x) ? x-->0+

A: Here we use the series expansion of the functions cos (x) and ln(1+x):

Q: lim x approaches 0 .............. (sinx)^2

A: Given:              limx→0 sin x2 Plug in the value: x = 0             =sin02

Q: lim 1- cos () X00

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

Q: 1-sinx x-1-cos2x 9) lim 10) lim TC X- sinx-cosx TL X- 4

A:

Q: lim X-3 Sinx X-0

A: Limit of a function

Q: limx>0+ (1/x- 1/tan-1x)

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Q: ((주)' lim x (1- cos () COs X->- 00

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Q: lim [(x²-In(x + 1)) cot x] x-0-

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Q: limit as x approaches infinity of (e^x + e^-x)/(e^x - e^-x)

A: Consider the given expression of which limit has to be calculated:

Q: 3. lim X-0 sinx sinx-cosx 4. lim x- 5. lim x(cosx-1) sinx-x

A:

Q: limx→0  (x^2+3) / (1−cosx)

A: given example is, limx→0x2+31-cosx

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

A: This question is based on limits of 0infinty indeterminate form.

Q: lim x→0+  ln(x) x

A: We have to find the right-hand limit of the following function   The function is lnxx   We have to…

Q: lim x→0 sinh x2 – x2 sinhx−x

A:

Q: lim x approaches 0 ................ (x^2 - 1)(2 - cos x)

A: To find the limit of the function as x approaches 0, the function is given as follows: x2-12-cos x

Q: lim xS0 cos2x - cos x / x^2

A: To find: limx→0 cos2x-cos xx2

Q: lim х-0 Arcsin x II

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Q: lim   ln(cosx) x → π/2

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Q: lim x>0 (x csc2x)/(cos5x)

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Q: Q5/ * lim (x-3)(sin-'(x) – x) using L Hopital Rule

A:

Q: limx→0  xcos(x)-sin(x)/x^3

A: Given: The limit limx→0xcosx-sinxx3, To find: The value of the limit.

Q: sechx+cshx b) prove that e2x cshx-sechx

A:

Q: lim 1- cos ( X00

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Q: limx>0 sin-1x/x

A: So, now we apply L' hospital rule to evaluate the given function. Because if we directly apply the…

Q: tanx Lim メーマ0

A: If we direct apply this limit  It becomes 0/0 form  So we apply d'hopital rule

Q: lim sin(5x) csc(3x) X-0

A: Formula: LimX→0[sin(ax)/x]=a

Q: lim sin(e-/) =

A: Given:limx→0sine-1/x2   The value of e-∞=0 and the value of sin 0°=0.

Q: (sinx -) (3sin²x -sinx +1) lim TE +X, 2

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Q: 1-sinx x²-49 b. lim x→7 x-7 lim C. lim X→00 x²+1 a. X 1-cosx

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Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

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Q: 2. lim x sin(1/x) X18 ex+2x 3. lim X18 ex

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Q: lim Jx-S

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Q: lim ( - x→0+ cot x)

A: We need to evaluate the limit limh→0+1x-cotx

Q: Lim Ln

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Q: Lim e^x +e^-x-x²-2/sin²x-x² when x approaches 0

A: The given limit is, This limit is in 0/0 form, so we can apply L’Hospital's rule,

Q: lim 3^x = 0 x--> -infinity, ε = 1/2, find smallest-magnitude N <

A: Use the definition of limit

Q: sin-1(x) – tan-1(x) lim 3x3

A: The given limit involves inverse trigonometric function as well as cubic function and the limit is…

Q: lim X-3 Sinx X->o

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Q: lim Vx2+1-Va²+1 4-, 5- lim 1 x+2 6-, lim sin 3x X-a -

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Q: +lim x-0 e -x - 8x ex - e x - sin x

A:

Q: tanx – lim 0 Cos[1 – –

A: Given, -limx→0cos1-tanxx

Q: Limit Sin 1/x x -0

A: Answer is mentioned below

Q: lim sin2x/ x            x---&gt;0 lim tanx/tan2x       x----&gt;0

A: Multiplied the numerator and denominator by 2When x-&gt;0 then 2x-&gt;0Answer: 2

Q: Find the limits

A: Given,                     lim(x,y)→(0,ln2)ex-y     And we have to find its limit.

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: limx→+∞ ( e^x+e^−x) /  (e^x−e^−x)

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Q: limx¬1 x(1 – cos-) x→1

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Q: lim cos xx x-0

A:

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.