e2t – e-2t – 4t lim t-0 t – sin(t) (use L'Hospital multiple times)

Q: [xus (2) x+10) xuIsx(p) x(1) (k)1 ×sinx (1x [x][a] (k) 1 x (m)xcosx

A:

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

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A:

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

A:

Q: x sin 4x b. lim x-0 1-cos3x

A:

Q: 6. (a) f(x) = arctan (e-2) 6. (b) f(x) = [arcsin (²)]³

A:

Q: Rx+2sinx Q2.a) lim sin (). sec (in 3+x

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

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A:

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A: Given:     limx→0+sin2x2

Q: e lim Secx-1 Sinx (-esux) 3}r® २5 ९६० 5x 2 lim ーD6 Sin5x of Sin4x. e lim メーD6 よ + tan 38

A:

Q: cos x lim Vx

A: Given: limx→∞cosx5x=?

Q: sech? (In x²) 15. f x/6 tanh (In x²) – tanh² (In x²) dx

A: I = ∫ sec h2 (ln x2)x6tan h(ln x2)-tan h2(ln x2)dx=∫ sec h2(2ln x)x6tan h(ln x2)-tan h2(ln x2) dx=∫…

Q: (b) lim ln(sin x) x→0+

A: b) limx→0+ln(sin x)

Q: x 0+ (d) lim (1 – 2x)¯4" -4x x→0+ (e) lim (sin æ)-In æ (f) lim (– In æ)*in æ sin x

A:

Q: 6y f) limy0 sin 2y

A:

Q: e-3sin z (c) lim x² (d) lim sin(rx) lIn (x – 1) x→1+

A: The given limit is: (c) limx→∞e-3sinxx2  To find the value of the limit.

Q: sin(6a°y³) =? lim a,y)→(0,0) xl12 + y4

A: If we put (0, 0) along the line y = m x3 , then,

Q: sinx Q1//A- f(x) = cosx x < Required: lim f (x) 4

A: To check the limit of the function at pi/4 , we check it's left hand limit and right hand limit at…

Q: x 2 sinx Q1//A- f(x) = x <= COSX Required: lim f(x) 4

A:

Q: x2 – lim x + sin x 2x x→0

A:

Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

A: Answer (7): The given function is y=x2-1sinhx+14 using product rule in differentiating above…

Q: 1. lim t0 sint sin(2t) 3. lim 2t 1- cost 6. lim sint

A: limx→af(x),  by completing a table of functional values. step 1: choose two sets of x-values—one set…

Q: solve using variation of parameters or reduction of order. (D2 + 1) y = tan x

A: Given (D2 + 1) y = tan x

Q: y2+sin y Lim y-00 y?+cos y

A: Given,          limy→∞y2+sinyy2+cosy

Q: (c) lim sin 3r sin 2r I sin 5z 8r-3 2r³ +z+1 (d) lim

A: Given that:                        (c) limx→0sin(3x).sin(2x)x.sin(5x)(d)limx→∞8x2-32x2+x+1

Q: sin(3t) i+ In(tan(6t)) -j+(t – 2) cos(3t) k , find lim F(t). t+0+ Let F(t) sin(6t) In(sin(3t))

A: solve the following

Q: 4. sin 5. y = x ArcCC 1 + v1-x² 2+X 6. y = Arccot x + Arctan 1-2x >| ×

A:

Q: 2 sin x 1 lim is

A:

Q: sin x 1) lim- 2) If f (x)=x +1 then the equation of tangent at x-2 is y-4x-3. d 3) dx -2 2

A: find limit using L hospital Rule    Since you have posted a question with multiple sub-parts, we…

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A:

Q: Find the limit

A:

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

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

Q: sin(2rx) lim x → 7 x2 – 49 -0.2857 T 0.2857 T -0.1429 T 0.1429 T

A:

Q: sin z coS T Q1-Solve by hospital rule lim

A:

Q: (1+sin2x)^1/x lim x approaches 0   So far I have broken it down to (ln(1+sin2x))/x and did the…

A: Let y= (1+sin2x)^(1/x)Then take ln on both sides.

Q: T+tan x 4. lim sin X→0 tan x-2 sec x,

A:

Q: h 1 lim h→0 2h sin(x² + 1)dx = -h

A: Here we will find out the required limit.

Q: sint lim t--0 t (A 1- cost lim t0 B t et – 1 . lim t-+0 t + sin t lim t-40 2 D t

A:

Q: 2-t+ sint 45. lim t+ cos t

A: We have to find he limit: limt→-∞2-t+sin tt+cos t

Q: 4 lim sin(x) х>0 х 41

A: Given that

Q: sec2x-2taпх lim X→T/4 1+cos4x

A: Consider the given limit limx→π4sec2x-2tan x1+cos4x   limx→π4sec2x-2tan x1+cos4x=00 Which is…

Q: x² – 9 2. lim x →- 3- x+3 (4 + h)² – 16 4. lim h-0 h sin2x 6. lim t tan³x

A:

Q: cos(x)-1 lim-0 sin(x) limx-0 %3D = 1

A: Substituting x=0 in cosx-1xwill result in indeterminate form 00. Use L'Hospital's rule,…

Q: lim y→0 sin3y/4y

A:

Q: sin(3t) lim t t→0

A:

Q: (x+n+ 1)³ – (x + 1)³ 2- dx lim n-0

A: Given: 2-dydx=limn→0x+n+13-x+13n