csch(1–x) lim (1 – cos-x x→1-

Q: Why does the lim as x approaches 0 of sin(x)/x = 1. We haven't learned derivatives so I wasn't sure…

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Q: - i) By using L'Hopital Rule, find sinx lim x-0 e3x 1 ii) Given that a = sin V3 2, find, csca -1

A: In L Hopital's rule take the derivative of numerator and denominator separately and than put the…

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: (1) limx-ol-cos x 2 sin²x (2) limx-0 x-³…

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Q: Find the limits. Are the functions continuous at thepoint being approached? lim x →1 cos-1 (ln √x)

A: We find the limit by substitution

Q: 4) lim 2Sinx – /3 = ? 2л - 3х 3

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Q: sin(2z)+7z2 –2z 25. lim =?(z+1)? 26. lim | (x-1) tan

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Q: Q3 :(A): By using "L' Hopital rules"; Find the limits of : 1 (1) lim,-ol1-cos x sin2x (2) lim,…

A: 3)1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0(tan-1x-x) /x3 Repost the next question.

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol 1-cos x sin²x (2) lim, o…

A: 3 1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0 (tan-1x-x) x-3

Q: te dt lim 0 x-0 sin x =?

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x sin²x (2) lim, o…

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Q: cos x 13. lim x→(T/2)* 1 – sin x

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Q: Q3: (a) Find the following limits if exist (without using L'Hopital's rule):- (2) lim,- tan r-sinx…

A: Explanation of the answer is as follows

Q: sin 3y lim y→0 4y

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

Q: lim b-> -0.1x e 1.

A: Let I=limb→∞∫1be-0.1xdx

Q: Q3: (a) Find the following limits if exist (without using L'Hopital's rule):- (2) lim, (3) lim,…

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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: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) limx¬(n/2)-(tan x)cos x (2) limx-o…

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

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Q: Find the limit of the given functions using a numerical approach 3. lim (2 cos x) 3T 4.

A: The solution of the problem is given in the next step.

Q: Find the integral.

A: Given,

Q: x-Arcsinx lim x3 1 lim X0 sin?x 1 x2

A: (a). We have to find:   limx→0 x-sin-1(x)x3

Q: F ind @ Dlim Ix16/ lim 1-cos 3x 9. 4-X lim (1-secx) lim CosO 9= (9 -) 2.

A: Note :- there is an error in part (a) in this part value of limit is wrong. So i am solving…

Q: 2. Calculate the following limits. Justify your answer. L'Hopital's rule Rule ) (without using 2x +1…

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x

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Q: (c) Prove the value of lim Sin 3a o Cos 4Do NOT use L'Hospital's Rule.

A: The given limit is,

Q: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x>0

Q: Lim as x approaches 0  1-cos(5x)+sin(3x)/x

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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: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim X x→0+

A: Solution: a) limx→0+sin xx1x2

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

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Q: cos x D. Explain why we cannot apply L'Hôspital's rule to evaluate lim x-0

A: Given query is to find why L'hospital can not be used.

Q: 1 Lim x→0* x0x 1 sin x

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Q: Use l’Hôpital’s rule to find the limits

A: Given: limθ→π22θ-πcos2π-θ for evaluating given limit, we substitute θ=π2+h so,…

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: Find the limit. sinx cos 4x lim x-0 x + x cos 5x A) 3 B) 0 C) D) Does not exist 4/5 -/2

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Q: cosx * sin? (3x) 2 2. lim x→0 x2

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: Find the limit. lim vx+11 cos (x + 3T) X-- 3T lim vx+11 cos (x + 3r) = →-3T Type an exact answer,…

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Q: Find the limits sin(3t) lim In(sin(3t)) i+ In(tan(4t))" j+tln(3t) A t→0 sin(4t)

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

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Q: 1+x-e* lim x→0 1-cos x lim(cos t)csct t-0

A: Given that: limx→01+x-ex1-cosxlimt→0(cost)csct

Q: I* cos z lim 1³+2

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Q: 1 lim x→0 x sin x x2 О 14 O 1/7 О 16 O 1/5

A: To find limx → 0 1x sin x - 1x2

Q: 4. Evaluate if they exist: (a) sinh x dx (b) lim , sinh x dx r+00

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x x→0+

A: We have to determine limit by useing l hospital rule

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x A 1.

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Q: 2y3 lim y→0 y-siny CSC X lim (secx + tanx)csc

A: