Find values of a and b such that sin 3x + ax + bx³ lim = 0 x3

Q: (2-4)* Q1: limx-1 sin(x³–1) x-1

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Q: 5. x sin 3) lim00 x+1

A: limx→∞x5sin5xx4+1=limx→∞ x5sin5xx41+1x4= limx→∞ x sin5x1+1x4 = limx→∞  sin5x1x1+1x4=limx→∞ 5…

Q: 2. Find if possible: sin(nx) a) lim x-4 x2-16 b) lim x (sinx+(cosx)³) (x2+1)(x-3) c) lim,--o (cosx)

A: a) Given that limx→-4sin(πx)x2-16we have to find the limit of…

Q: (2) 1: limx-1 sin(x3–1) x-1

A: limx→1 (2-1x)2sin(x3-1)x-1=limx→1 (2x-1x)2sin(x3-1)x-1=limx→1 4x2-4x+1x2sin(x3-1)x-1=limx→1…

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: tan x lim 3) Vx+1-1

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: Q4: A) solve: 1+xsin 1) lim- y0 1+xcos sin 2) lim -2m 20-4

A: Note: We are entitled to solve only one question at a time. To Find: i. limy→01+xsin1x1+xcos1xii.…

Q: -1 sin (5x) lim

A: The given expression is limx→0sin-15xx the given expression is the indeterminate form 00 Apply L'…

Q: Q3) Find: (1) lim, 1+cos 2x (2) limx→-2- (x + 2) |4-x²| 2-x

A: Q3)1Here, we need to calculate the limit of ,limx→π21+cos2x4x-π2

Q: b) If x sin x 2 - 2 cos x hold for all values of x close to zero. Find limx0 xsinx ? 2-2cosx

A: Given, limx→0xsinx2-2cosx

Q: æ In(sec(2æ)) (sin(3x))³ lim x→0

A: Given,             limx→0xlnsec2xsin3x3

Q: Find the value of Tx³ + 2. lim [sin x3 + 1 -1 1 O O

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

Q: 3* Evaluate (a) lim sin y and (b) lim y x-1 Vx +5

A: we have to evaluate the following: a)  limy→π3 siny b) limx→-13xx+5

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO FO x-5 • lim х-5 х2-25 = 10 FO

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Q: (:) -*) Evaluate: lim 1 ба" sin 6.

A: Topic-limit calculation

Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

A:

Q: ,3x lim x→0 CO cosh(Зa)

A: By substituting cosh(3x) in givenimit we can get the required value of Function.

Q:

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Q: 2 sinlbx) +1-cosX lim

A: Given,           limx→02sin4x+1-cosxx

Q: 2 lim (cosx)x² =?

A: We have to find the limit

Q: Find lim. Sin (X/y X-T/4

A:

Q: Show that lim [x2 sin (1/x)] = 0.

A: Given: limx→0x2sin1x

Q: lim,-o ([sin x]*) is

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Q: Evaluate the limit: sin(13x) lim I-0 tan(7x)

A:

Q: (a) Show that tan x = sec?x using quotient rule. dx x+8 (b) Find lim X-2 x+2

A: Solution-

Q: Evaluate: lim   (1−cos−1x)csch(1−x) x→1−

A: We have to find the limit.

Q: In(sin 4x) \ In(sin 8x) lim x → 0

A: We have to evaluate the limitlimx→0ln(sin4x)ln(sin8x)

Q: 4x(1 — сos(x)) lim х — sin(x) х>0

A: Because the limit is in 0/0 form. Apply L'hopital's rule.

Q: sin x 34. lim 1 - x o0-r

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Q: Clearly explain why lim (sin-(t) is equal to 1 and not zero. t+0+

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Q: Find the two limits: sin 2x lim r-T/2 COS x

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Q: tan nx 3) lim x→0

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Q: 2tan 'x -x (-) 2x – sin 'x 02. lim, -1

A: Given limx→02tan-1x-x2x-sin-1xTo evaluate the limit:

Q: tan(31x) lim x → 0 5x

A:

Q: -2x – 1 Find lim X+0 sin 3 sin()

A: Using formulae of limits

Q: 2. Evaluate cosxsin2x lim 1 – sinx

A: We need to find limx→π2cos x sin 2x1-sin x Now, put the limit in the function, that is put x=π2 .…

Q: Find lim sin (4 T x). I -3

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Q: 5 sin(6x) lim x→0 3x

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Q: х(4+sin 6x) 3. lim X→+0 х+1

A:

Q: 7x( cos (4x) – 1) Use l'Hôpital's Rule to evaluate lim sin (5x) – 5x

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Q: 7. *Find the values of a and b lim sin(ax-2a) x-2 = 3 %3D x-2

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Q: 2tan x- x lim, -1 2х -sin " x,

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Q: Evaluate limt-->0 (sin 3t)/(sin 6t) WITHOUT using L'Hospital's rule.

A: The given function is limt-->0(sin 3t)/(sin 6t).

Q: lim as x goes to 0 (sin(2x)+7x2 - 2x / x4 + 2x3 + x2)

A:

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: Which of the following will make limx→c f(x) and f(c) equal? limx→2 : (x²+x-6) limx→–1 (x³ − 2x + 3)…

A:

Q: Evaluate

A: Our Aim is to evaluate the limit given below:-limx→0tan (2x)x-(i)