2) Show that sinax _a lim x-0 tanbx b %3D

Q: Compute lim x-T sinx

A:

Q: Determine the limit: 12 x+ 1 tan(2 x) lim 3 sin(3 x) X- 0

A: Given limit: limx→012x+1tan2x3sin3x

Q: Calculate the limit limx→0+(arcsinx)2x.

A:

Q: 2 xt (* sin) lim sec x lim X→+0 X. 2

A: Given limits are  1) limx→∞xsin2x2)limx→π2secx3)limx→0sinxx

Q: sin(51x) lim 16x

A:

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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: tan (5x) x sin3 (2x) 2)- limx-o:

A: we have to evaluate the A=limx→0tan4(5x)xsin3(2x)

Q: Q5/ * lim (x-3)(sin-'(x) – x) using L Hopital Rule

A:

Q: Use L'Hopitals's rule to find lim →号 tan x n · 4/(2x-T)

A: L hospitals rule

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: 3x tan(2x Use L'Hopital's rule to evaluate lim sin(4x)

A: Using l hospital rule we have

Q: 1-cosx 16. lim X-0 3x sin x

A:

Q: 5. Use L'H rule to find (a). lim Inz2 (b). lim (sin x)(In x).

A:

Q: Evaluate limx-->0 (tan 9x)/(sin 4x) Without using L'Hospital's rule.

A: Obtain the limit without using L’Hospital rule as follows.

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: by L'Hopital's rule 1-cos(x) lim x2

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Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

A:

Q: Evaluate limx-->0 (sin^2 2x)/(2x) Without using L'Hospital's rule.

A: The given funtion is (sin^2(2x))/2x for the limit x tends to 0.

Q: tan(1 – x) 2 limx→1 2x +x – 3

A:

Q: lim (sec æ)cot is エート

A:

Q: Use L’Hopital’s rule to show that limx→π/2 2 tan x/sec2 x = 0

A: Use L’Hopital’s rule to show that limx→π22tanxsec2x=0

Q: Use L 'Hopital's Rule to find the limit:

A: Given limit is Therefore, given limit is of indeterminate form

Q: tan 7x i) lim x+0 sin 3x sin(x2 + 3x + 2) j) lim x+2 x + 2

A:

Q: 1-cos 2x sin² x limx-0

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

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

A:

Q: lim * In(sec(2x)) x→0 (sin(3x))³

A: To find the limit.

Q: Show that limx→0(√x) cos(1/2x) = 0.Show your work.

A:

Q: sin(4x) lim x→0 sin(8x)

A: To find the given limit

Q: 3 (e) lim (1 x2

A:

Q: Find lim 1-CoS 3X Xう。 tan x -1 lim メー X - X->

A: Solution is given below..

Q: solve using L'Hopital's Rule 2. Lim      (x-sinx) / (x^3)    x->0

A: To find: The limit of limx→0x-sin xx3. Calculation: Apply L'Hospital rule: limx→0x-sin…

Q: 2.) lim cot x- sin 2x cotx-1 3.) lim x0 cotx+1

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Q: tan(4x) lim sin x [Hint: Use the fact that lim,→0 = 1.]

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: Find the value of lim tanx

A: As per our guidelines we only solve question number 1 . If you want the solution of other parts…

Q: Investigate limit x 0 sin(pie/x)

A: Here we need to find the following limit:

Q: Show that lim x sin l/x = 0.                   x→ 0

A: It is known that the absolute value of sine function is not greater than 1, then  -x≤xsin1x≤x

Q: Use the L' Hopital rule to solve: lim x->0 2sinx-sin2x/x-sin x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 1- cos 3x lim &r

A:

Q: Lim sin x X0 Cos 2x -cosX

A:

Q: Evaluate lim wing sin2x +7x²-2x Wir 'Hopi L'Hopital's rule,

A: Consider the given expression. limx→0sin2x+7x2−2xx2x+12 Simplify the denominator.…

Q: Compute limx→0 sin(x) − x divided by  x^3

A: We have to evaluate the limit: limx→0sinx-xx3 After putting limit value we can see that this is 00…

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: sin(3x – 3) lim x² – 1

A:

Q: 1 (sinx\1-cosx lim X→0

A: We need to evaluate limx→0sin xx11-cos x Let y = sin xx11-cos x Then log y = 11-cos x log sin x…

Q: Find lim Sin 3x (1- Cosx) メーや。 メ*s X Sinzx cosx

A:

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…