eax lim x → 0 In(1+ bx) -ах e

Q: lim x→-0.5- Vx + 1

A:

Q: lim (1-e X-

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

Q: lim 1- cos () X00

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

Q: lim x→-0 e-x

A: Given: fx=limx→-∞x2e-x

Q: lim tangx X->즐 (쫄-x n2.

A: Given: limx→π2tan2xπ2-x 00 form If limx→afxg(x) is of the form 00, then we use L'Hospital's rule.…

Q: evaluate the limit.

A: Given:

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

A: Here we have to evaluate the given limit .

Q: x sin a-asinx compute lim X-а

A: To find the given limit x=0 then [0sina-asin0]/(0-a) 0/(-a) 0 So, limit is 0

Q: lim x- Vx x-0

A:

Q: 23. lim (1 + x)cotx

A: As you have asked for question 23 only. So I am solving that only.   Let f(x),g(x) be two functions…

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

A: The solution are next step

Q: (2 -1) s lim z

A:

Q: lim [(x²-In(x + 1)) cot x] x-0-

A:

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: பாதுக lim sec 20 ー1

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: Evaluate

A:

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

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

Q: e- lim

A:

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

A: Topic = Limits

Q: Lim e-ex TEX

A:

Q: lim 17) P - (5, 5, 1) In (z\x2 + y²)

A:

Q: lim x to (0) cosecx - cotx

A: Find the limit as follows:

Q: lim of xx^(1/2) as x approaches 0+

A: Given a function:

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

A:

Q: sin(x²) x→0 In(cosx) 4. Evaluate lim

A:

Q: Lim 1- Cosx て X-)0

A: Given: L=limx→01-cosxsin2x We know that 1-cos2x=2sin2x…

Q: lim 1- cos ( X00

A:

Q: a Exponential limit Prove that lim (1 + e", for a + 0. %3D

A: Given limx→∞1+axx=ea, a≠0

Q: sinx Example 11: lim nx X X-

A:

Q: 1. lim x²-1 al 2. Tく-X b) lim X-Sin 2x +3 c) lim Vey?-x

A: Given- limx→1x2-1x10-1

Q: السؤال 1 lim iz?-z z-- z2-1 i o -i O 1 0 -1 O

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: 2. limx-co √x √x+√√x+√x

A: Here we have to find the value of  limx→∞xx+x+x

Q: lim Jx-S

A:

Q: 1-Vx+1 lim x-ol Vx+9-3.

A:

Q: lim 6x e-* i

A:

Q: sin(nt lim In z 1 lim (1+

A:

Q: ure E-S theorem to prove the following lim (9x+5) = - 32. x→3

A: Here we will evaluate the required value.

Q: 4xy lim Compute the (xy) (0,0)

A:

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

A:

Q: 3. lim- im:-) (x+r)²

A: Given: limt→02t5(x+t)2-5x2

Q: lim %3D X2 -マメ

A: The solution for the above question is as shown below.

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

A:

Q: lim lx-1| х>1 1-х ?

A:

Q: Lim ģ G メ-ム

A: We have to use L' Hospitals rule ,if we get any indeterminate forms (00,0×∞, ∞∞,∞,-∞) when we…

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.