sin-1(e* 2 lim V1 - e2x x→0-

Q: 1 (a) lim 2x+sin x 5x+2 (b) lim 1 (c) lim cos -

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: lim (cos(9x)) (+) +0+x

A:

Q: cos x dx - In (1 +x) 1- cos x a) b) lim

A: Given: a)∫011-cos xx2dx b)limx→0ln1+x21-cos x

Q: sin 3x + ax + bx3 lim %3D x3

A:

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

A:

Q: 1-sin t lim 1+cos 2t t- 2

A:

Q: lim x approaches zero, sin4x/sin3x

A: Given,

Q: sin x 3. lim х-30 1 — соSX

A: L Hospital rule

Q: Find the limits

A: Given: Function  To Find: Limit of the function at the given point

Q: Use series to evaluate the limits in Exercises

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

Q: e* +e* -x? -2 1) Lim sin² x – x²

A:

Q: sin(2x) limy→ 0+ X

A: Given:     limx→0+sin2x2

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: 1- Cos(ux) lim x-)0

A: Given expression limx→01-cos4xx2 Recall the identity 1-cos2x=2sin2x limx→02sin22xx2

Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

A:

Q: Lim x-0 e³ +ex -x²-2 sin² x-x²

A:

Q: sin3x d) lim x→0 + lim cos x + lim 2x² x→2 x-3

A:

Q: sin 1(e") 2. lim (- V1-e2

A:

Q: Evaluate the limit.

A: Given that, limh→0sin(2h)(1-cos h)h2 Because of the direct substitution of h = 0 into this, we get…

Q: limx→0  xcos(x)-sin(x)/x^3

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

Q: e) lim 1-cost sin²)

A:

Q: (b) lim ln(sin x) x→0+

A: b) limx→0+ln(sin x)

Q: sin 5x. lim X0 5x. Cos 5x

A: Given limit, limx→0sin 5x5x·cos 5x

Q: lim-o t- sin 3t² 1-cos 2t

A:

Q: xn²+1. lim, cos( x0 cos(*+1) x² +3 limx→0+ *国

A:

Q: 2 |-cos X lim b. X - Sin x

A:

Q: lim a sin(1/2),

A: Given,           limx→0xsin1x

Q: sin(3x – 3) lim x² – 1

A: Given :

Q: 3. lim, 2x e²x-e sinx -2x

A: Given limit limx→0e2x-e-2xsinx The objective is to find the limit.

Q: 3 lim z? sin(-

A:

Q: lim -Vx + +sin(x)cos(x) 1+In (x)

A: Topic:- limits

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

A:

Q: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

Q: (x-sin x) A- Find lim,-0 1-cos X/

A:

Q: (2-4* limx-1 sin(x³–1) X. x-1

A:

Q: sin5x(1-2t)dt (6) lim

A: limx→0∫xsin5x1-2tdtx Let  I=∫xsin5x1-2tdt=t-t2xsin5x=sin5x-sin25x-x+x2

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 Cos t X-2SM X2

A: limx→2cosπxx-2sinπx

Q: et Lim x-0 +e³-x²-2 sin² x-x²

A:

Q: 1 - cosh x lim x→0+ ln(x² + 1)

A:

Q: ¶/x x-0 sin (1 /x) Lim

A: To evaluate: limx→∞π/xsin(π/x)

Q: Find the limits

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

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

A:

Q: lim t→0 of tan4t/sin2t

A:

Q: 2x e* –1 lim- x→0 sin (2x)

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: lim cos xx x-0

A: