If CR is the contour z = Re" for some constant R>0 where t e (0, 4, first prove that e dz <(1 – e *). What can you conclude as R→ o0? 4R CR Remark: You can use the inequality sin(2t) > 4t for all t E (0, 4] without proof. 2z + 1 - Evaluate dz; state which results you use! COS Z 22

Q: Letr> 2. Show that sin² r - sin² 2 r-2 < 2. Justify your answer. Hint: Apply the Mean Value Theorem…

A: Let r&gt;2.   To Show: sin2 r-sin2 2r-2&lt;2.

Q: Find the domain of y = cos ¹(2x).

A:

Q: 5. Evaluate: 34 l vo dx dx. √9-16x2 0

A: To find the value of given integral.

Q: 9. y = C,eax cos(bx) + C2eax sin(bx); a and b are parameters

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: 7. Let f(x, y) = 10xy* + x°y². Find fyyy. 4

A:

Q: The principal part for a) 5 b) 2 for xo of f(x) = 2 + 5+ sinx with respect to ↓

A: Given that .Let .We need to find the principal part of f(x) with respect to g(x) as x→0.We will use…

Q: Show that sin x < x for all x ∈ (0, 2π).

A:

Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

Q: (5 + sin r)e 2. If y = what is dy/dr? 12 - 7

A: Use basic identities of derivatives.