13 By considering the Maclaurin expansions of sin(kx) and cos (kx), k constant, evaluate if possible sin(kx) (а) lim x-0 cos (kx) – 1 (b) lim sin (kx) (c) lim X0 1- cos(kx)

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A:

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A: We need to evaluate : limx→π4sin2(x)-cos2(x)sinx-cos(x)

Q: 31. Use the identity x + y y sin x + sin y = 2 sin cos 2 to prove that sin(h/2) cos h sin(a + h) –…

A: Given information: sinx+siny=2sinx+y2cosx-y2 To prove: 1: sina+h-sina=hsinh/2h/2cosa+h2

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

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: Expand the following functions in terms of Legendre polynomials: (a) 35 (cos 0)4 (b) cos0 - (cos)³…

A: As per the norms, we will be answering the first three subparts. So, if you need an answer to others…

Q: = lim Δx=0 Prove that the result is equal to cosX sin( x + 4x) – sin x Δε

A: To find:-

Q: 3. lim cos →** x+7x²-√√5 x-x'¹

A:

Q: (d) lim 1 - cos(x²) x0 x² sin² x

A: Plug in the value of x = 0