lim * In(sec(2x)) x→0 (sin(3x))³

Q: Find the limit of sin(6x) limy→0° sin(2x)

A:

Q: 3-v49 B) Without using L'Hopital's rule, find: lim

A:

Q: 9. Lim 6x - Sin 2x メ→0 2x +3sin 4X b. lim x²-1 1/2

A:

Q: lim (In(x))½ ?

A:

Q: Find the limit: Lim x-->0  2 sin2 3x / 3x2

A: you know that:

Q: Lim secx -co tx メーマ

A:

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: lim In x X-→ 0+

A:

Q: lim at e -

A: Find the limit when x tends to 0

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

A: Here we have to evaluate the given limit .

Q: 1+x V1-x sin-1(x) [3] limx-0

A: To evaluate: lim[x→01+x-1-xsin-1(x)] Solution: lim[x→01+x-1-xsin-1(x)] On simplifying further we…

Q: (1 cosr)dt 1. limx-0 2x -?

A:

Q: Зx2-14х +8 lim 7x-28 x+4

A: By factoring method: Take factors in numerator and denominator  Limx-4(3x2-14x+8)/(7x-28)         =…

Q: 1-cos 2x lim x→0 x2

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

Q: lim In(r) - 0t

A: Consider the given limit

Q: Find the limit: Lim x->0  2 sin2 3x / 3x2

A: Given,         limx→02sin23x3x2

Q: Why can't L'Hopitals Rule be applied to evaluate x - cos x lim x→+00 x + sin x

A: We have to explain about the given information

Q: lim X(In x)2 requires repeated application of L'Hopital's rule. Show all the steps.

A:

Q: Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim x4 (Vx+5)-3

A: We need to find the limits of the given expressions by using the L.Hopital rule. For (1),

Q: Find the limit of * sin(6x) limx→0 sin(2x)

A: Given problem is :

Q: Evaluate without use of Hopital's rule: tanx-sinx 1) lim-0

A: using expansion of trignometric function

Q: Solve without L'Hopital's rule. lim x→1 [tan(1 − x)] / (2x^2 + x − 3)

A: We have to find out limit

Q: 2 2- limx-1 sin(x3-1) x-1

A:

Q: 1 () X. lim х+ sin X→+∞

A: The objective of the question is evaluate the limit of the given function.

Q: sin(x – 3) lim X→3 + 6x – 27

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Q: lim x In(2x) x→0+

A:

Q: b- lim [In(cos(x))]= x->0

A: Given that:limx→0[ln(cosx)]x

Q: x- cosX X- COS X 4. lim,

A: Our Aim is to evaluate the limits given below:-limx→∞x-cos (x)x-(i)

Q: 4. Use L'Hopital's rule to evaluate sinh(2) lim x+0 sec(x) - 1

A: we have to evaluate  limx→0sinh2xsecx-1=00 It is known that ddxsecx=secx tanxddxsinhx=coshxddxtan…

Q: tan(1 – x) 2 limx→1 2x +x – 3

A:

Q: tan(1 – x) limx→1 2 2x +x – 3,

A: Limit

Q: If x sinx < 1 2 - 2 cos x hold for all values of x close to zero. Find limx¬0 xsinx ? 2-2cosx

A: 1-x26&lt;xsinx2-2cosx&lt;1 holds for all values of x close to zero. Now, limx→01-x26=1-0=1 &amp;…

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

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Q: Compute lim 2>0 sin x O 2 O-1 1 undefined

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Q: Find the limits limx→0+x-1/ln x

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Q: lim (In x)

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

Q: lim (sech 2x)csch x x² +0+*

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Q: (1) lim,o In (sec x) 3x (2) lim, (tan x)*

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Q: 3. Find the limit. tan(5x) 0 sin(3x) sin(6x) (2) lim x04x-5x (1) lim

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Q: se Ľ' Horpitals Rule to find X>0 lim e2x_I SInX

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Q: sin(4x) lim x→0 sin(8x)

A: To find the given limit

Q: (i) Evaluate In (1-z³) lim 2->0 sin (2z

A: We need to evaluate the limit If the value of the function after putting the limit is in the…

Q: TD - xs3もーな x sin"x Lim ×→の

A:

Q: Find lim x→-3 sin(−4 π x)   lim x→-3 sin(−4 π x)

A:

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

A: Topic:- limits

Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

A:

Q: Evaluate exactly lim (1 + sinx)²cotx x→0

A: This question is indeterminate form of 1infinity and solved using L Hospital rule.

Q: 2. limx-co √x √x+√√x+√x

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

Q: 7- sin-(e*) 2 lim V1 - e2x

A:

Q: 2- x - sinx 1. lim x00 x + cosx x*+2x-1 2. lim-0 x3-2x2+x

A:

Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

Q: lim In(10x) x-0t

A: To find the below right-hand limit.

Q: 2x cos. X 17) lim --

A:

Q: how do you express lim,,→ Li=1 Σ! as п 1+ definite integral

A: We know that

Q: Q2: (a) By using " L' Hopital rul (1) limx¬(1/2)-(tan x)cos x

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Q: Calculate lim-x+sin x x0 -1+ cos x

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Q: lim sin (xt3) dt X 5

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Q: cos 3x – cos 2x - Evaluate limx→0 x2

A: Consider the given function, limx→0cos3x-cos2xx2 applying the limit to the function we get,…

Q: Compute limx→0 sin(x) − x / x^3

A: To find the limit, simplify the expression and then apply the limit to each term in the expression.…

Q: lim Vz+6-V6

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Q: lim as x→0 of sin(x4 )/x

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Q: 2х а) lim -1-2x (sin 2x)+² - et b) lim -4x - cos x

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Q: limx¬1 x(1 – cos-) x→1

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Q: Find the value of limx→0 sin(sin x)/x

A: L'Hospital Rule: According to this rule limit of the intermediate form 00  or  ∞∞ can be solved by…

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

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Q: B) Without using L'Hopital's rule, find: lim 3-Vx2+9 x2

A: