lim x1/x X→00 lim x→1+ [ln x х-1] lim (x + 1)cotx X→0+

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: 7) lim (Ln(x) – x) X→∞

A:

Q: lim 1- cos () X00

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

Q: Ln(x – 2) - 5) lim X→2+ x-2* Ln(x2 – 4)

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Q: lim x→0  2 ln x.

A:

Q: 6) lim (x – Ln(x² + 1)) X - X→∞

A: Here I am attaching image so that you understand each and every step.

Q: sin 3x lim .2 x0 4x -x

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: 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     ln(2x4+8x)-ln(5x3+7) x → ∞

A: Topic:- limits

Q: lim х-0 Arcsin x II

A:

Q: lim x to (0) cosecx - cotx

A: Find the limit as follows:

Q: lim   ln(cosx) x → π/2

A:

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

A:

Q: lim x->0^+ square root x ln(x^3)

A: To find,

Q: Lim (x+1)ot* cot x x - 0

A:

Q: sin 2x d) lim- x+0 sin' 3x e) lim- x-0 tan' 2x 2 tan x f) lim- x-0 x sin 3x g) lim- sin 5x i) lim-…

A:

Q: x2-4 1) lim x-2 x-2 sin 2x 2) lim 1 1 3) lim(-- X-0 x VX

A:

Q: sin 5x i) lim- x-0 sin 6x sin 3x g) lim x-0 x sin x h) lim- x+0 7x sin 6x j) lim- x-0 6 sin 3x k)…

A:

Q: lim 1- cos ( X00

A:

Q: lim x→0 tan2x-2sinx x3

A: A detailed solution is given below.

Q: lim x-0 tan x - x .3 X

A:

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

A:

Q: lim X→+∞ 5 In³ x 2 X²

A: Let's evaluate limit.

Q: lim COos x –1 x→0 x² – x³

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

Q: lim x→∞ [ln(8 + 3x2) − ln(1 + x)]

A: We have to find the limit.

Q: Find the limit

A:

Q: sin (x-1) lim x+1 x2+2x-3

A: To evaluate: limx→1 sin⁡(x−1)x2+2x−3 The given limit is of indeterminant form 0/0

Q: x+6 lim x--6t x+ 6 lim x6 x6 Jx 6 lim x6 x6 =

A: If x-> -6^+ then x>-6That means x+6>0So, |x+6|=x+6Answer(a): limit x-> -6^+ |x+6|/(x+6)=…

Q: sin 2x 2. lim- X0 2x+x

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Q: lim.                          x^5 x --> - infinity

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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

A:

Q: Lim (1/x² – 1/x² sec x) X – 0

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Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

A:

Q: 26.lim(1 + cosx)2secx x 2 27.lim (G– x) tgx 27.lim ( - 2

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Q: lim x approaches infinity x1/x

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Q: Lim Ln

A:

Q: sin (x-5) lim x→5 x -8x+15 ||

A:

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 x->0 (x2 +x)

A: Given,          limx→0x2+x

Q: sin x x0 sin Vx sin (x2 + x) 26. lim 28. lim sin (Vx-3) 30. lim x - 9

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

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 -> 0    ln(1+x)-x / 1-cosx   = ?

A: To find lim x -> 0    ln(1+x)-x / 1-cosx   = ?

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

A:

Q: lim x (1 – cos X→-0

A: limx→-∞x1-cos1x

Q: 1 - cosh x lim x→0+ ln(x² + 1)

A:

Q: lim x->0  ((1-x^2)/(x^2))^(tanhx)    using l'hospitals

A: Use l'hopital rule

Q: iv. lim 1- Cos x X->0 v. lim tanx X->0

A: We want to find the limit of the given expression. If we substitute value of the x in expression…