(e* – 1)? lim I-0 x sin x

Q: e* (1-e*) lim,0 (1+x) In(1–x

A: Given problem:-

Q: 1- cos x The lim X40 sin x is equal to O 2 Zero O-

A:

Q: et +e-& – 2 Evaluate L = lim Hint: use L'Hospital's Rule. 1- cos x |

A: Use L hospital rule

Q: e*(1-e*) (1+ x)[ In(1–x)] 12. lim, 0 'x0

A: Recall: If we have 00 form then we apply L'Hospital Rule.i.e, limx→a f(x)g(x)  = limx→a f'(x)g'(x)

Q: 1— 2 — е-7 lim 2.x e sin(8x) →-

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: If L = lim x-18 x+ sin(+1) 1 + [x/³ ( and M = lim x→0 of L + M + 11. (172) 1 + 1² sin 2x tan-1 dt…

A: Here we will use L'hospital rule     limx→a fxgx  in 00 or ∞∞ form =limx→a f'xg'x   and Lebnize rule…

Q: 1 Evaluate the lim sin x>0

A:

Q: 1 5 arctan x/ = ? Use L'Hospital's Rule 4 lim 4 arctan-

A:

Q: lim (x)-(.0) tan , -= (A) Does not exist (B) e? (C) 0 (D) ezn (E) e *IN

A:

Q: sin(1 – t) |2 – 2t| (b) [8 marks] lim t+1-

A: this is left hand limit then limit approaches from left side

Q: 1+sin x-cos x Find limx→ а. 0 b. 1 c. +0 d. -00 e. None of the above

A: We will apply L' Hospital rule for indeterminate forms of limit

Q: -2x lim (e cOs x) х) x → 00

A:

Q: e* +e* -x? -2 1) Lim sin² x – x²

A:

Q: Show necessary computation x²-9y? lim (x,y)→(1,0) tan-1 (x4 – 4xy + y²) lim (х,у)-(0,0) х-Зу b. а.…

A:

Q: lim - 1, avx + 3 – b x - 1 lim If score А. 4 D. В. 2 С. 1 E. -INI14

A:

Q: 27. lim (x + cos

A:

Q: i) lim e5x cos x 个。 ン

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

Q: x* –1 lim 6 sin x For B = - which one is B? x→0+

A: We have to use series expansion here.

Q: Find the limits

A:

Q: Q\ Find lim tan(x)cos(x) O 2 -1

A: The given limit is of the form ∞0 form. Let L=limx→π2-tan xcos x⇒ln L=ln limx→π2-tan xcos x…

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

A:

Q: 1. 5.lim cos(x) sin(x)

A:

Q: lim,-0 e" = ?

A: Consider the given limit limx→-∞ex.

Q: 1 + cos(x) a) lim %3D 20 -x ) lim x-1( In(61x-60)

A: Given, limx->π (1+ cos (x))/(6(x-π)²) = (1/6)limx->π (1+ cos (x))/((x-π)²) = (1/6)limx->π…

Q: et - e* lim,0 2 sin x

A: Consider the given function, limx→0ex-e-x2sinx put the value of limit into the function,…

Q: |- lim メ→ X-3 2. lim メ→2 (会 4 メー2 メ*-4 3. lim メ→。 3メ - S;u4X 4. lim メ→。 tau3X 5- lim 1- Cose Sin'e

A: Since you have asked multiple questions. So, we are solving first few for you. If you want any…

Q: 1 – x6 (d) lim x→0 1 – cos (x6) ||

A:

Q: x²+3x (t – 1)e' dt 2л — 4 - lim x→2

A: Given limit is : limx→2∫10x2+3xt-1etdt2x-4dt To find the value of limit by using L’Hospital’s.

Q: 1 1 7. lim X-0 (Arctanx)² x2

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: (b) Write lim > sin n as a definite integral on the interval [0, 7]. Use this definite integral to…

A:

Q: (d) lim (e) lim (1 – sin(x))/-

A:

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

A: We have to evaluate the following limits

Q: tan(xy) = ? lim .2. (х.у) >(0,1) х*у+x 1 1 (b) 1 (e) (d) - (а) 0 (e) 1 4 - |3

A:

Q: 1 4. Find limx→0+ ( ) ex-1

A: Given :          limx→0+1ex-1-1x

Q: 5. Find the length of the curve x =y? +2} from y =0 to y = 3. In(5x+2). In 3x 6. Solve lim

A:

Q: 8. Evaluate e8x - 1 lim sin (6x)

A: See the attachment.

Q: Q5:The value of: * sin (5x) lim I-0

A: We have to find the value

Q: 1. lim 3" 2. lim 5* 3. lim log r エ→4 4. lim cos r

A:

Q: (x+h)³-x³ lim h→0 h. sin(3w) lim w-0 2w sin(h)(1-cos(h)) lim

A: We know (a+b)3 = a3 + 3a2b + 3ab2 + b3 limx→0sin xx = 1 limx→01 - cos xx = 0

Q: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

Q: 399. [T] lim e(x - 1) x-1 x-1

A:

Q: (1) limr-(n/2)-(tan x)cos x (2) lim,-o x-3(tan-x-x) (b) If у %3D 4u?-Зи + 2 %; и 3 е* + 2e2х, find…

A: For other questions reupload according to bartleby guidelines

Q: e* + e-x – x² –- 2 lim sin? x – x2 х — x→0

A: To evaluate: The limit limx→0ex+e-x-x2-2sin2x-x2. Calculation: Use L'Hospital rule to evaluate the…

Q: 73. lim In(cos x)

A:

Q: Q5 100 5+2³+ [In(In r)] lim a) 1+ 7 +6² + [In(In x)]200 cos x ln(x-7) *-+*+ In (e-e) b) lim

A:

Q: 1 x |=? Use L'Hospital's Rule 4 lim- 5 arctan -4 arctan 5 xVx

A: