39. Does not exist; cos e – 2 lim 00- cos e – 2 lim 00+ and

Q: Solve

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A: We , have                Given      lim 1-cos3x1+3x-e3x     x70We have to evaluate the…

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A:

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A: cos x = x   rearrange to x - cos x = 0

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A:

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A: The given function is: The general form of the cosine function is: where, |a| represents the…

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A:

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A: Here I am attaching image so that you understand each and every step.

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A:

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A: This is 0/0 form so use L hospital rule and Solve.

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A:

Q: 1- CoS T lim 30 r In(1+ z) is

A:

Q: 2 Prove that lim x*cos 0.

A: Explanation: Given that,  limx→0x4cos2x=0     Taking LHS(Left Hand Side) limx→0x4cos2x

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A:

Q: n+1 Evaluate lim cos“(x²)dx n→∞ (and show all work)

A: The required results are as follows: cos2 x=12+12·cos(2x) and cos 2x=1-(2x)22!+(2x)44!-(2x)66!+...…

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Can you show me a step-by-step proof

A: We need the following two identities to produce the required prove:

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Q: Evaluate using the result of Exercise 54

A: Given: limh→0cos3h-1h2 we know that 1-cos2θ=2sin2θ…

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A:

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A: Consider the Bessel function, Jnx=xn2n Γn+11-x222n+2+x42·42n+22n+4-…             ...1 Substitute…

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A: Given that: limx→0ln cosxln cos(3x)

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A: Given, Cosx =x

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A: We can prove given result by mathematical induction: Define a statement p(n).  Show that p(n) is…

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Q: 4) dr In((3x² – 4x + 7)(5x³ – 9x)®) Hint: applying properties of limits will help you avoid using p…

A: Given, 4) dln3x2-4x+75x3-9x8dx  5) dcos4x2-5dx  We have to differentiate it.

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A: Given

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Q: Below are the graphs of y = 1+ sin 2x and y = (sin z + cos x). %3D 3. -2- -1- TT 2TT -1- MAR 75 (9)…

A: Point out the points Then find where the curve is zerro

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A: To prove : y'' =0

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Q: (a) Show that lim | x| cos = 0.

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: (d) Show that there is some x with 0 < x < 2 such that x2 + cos(ax) = 4. %3D

A: Solution-