30.3. Find and classify the isolated singu ons: 2³ +1 2² (z - 1)' (b). 2²e¹/², (c). Z COS Z

Q: (a) cos(iz) = cos(iz) (b) sin(iz) = sin (iz) for all z; if and only if z = nлi (n = 0, +1, +2, ...).

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Q: Determine the values of n and h required to approximate e²x sin² (3x) dx to within 10-4 using (a)…

A: Given the integral We need to find the values of n and h such that the error is within 10−4.(a) The…

Q: 2. Which of the following functions is of exponential order? * 4 f(t)= Sin 4t f(t)= 5{VT + A.) O B.)…

A: The function of exponential order is determined as shown below.

Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: . Fing the coefficient of x' and x' 9 10 expanston of any x in the (22- * Find the qe from of (2+ -5…

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Q: I If y = 2 cos x + sin 2x, find y" at x = - x=27/17-

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Q: 4.82. Show that f/2 sin² z dz= f/² cos² z dz = π/4.

A: To show that, ∫0π2 sin2 z dz=∫0π2 cos2 z dz=π4.

Q: 2+7 sin cos z zp-

A: Given: ∫2+7sin3zcos2zdz

Q: 1. Lif f(x,y,2)=2exp(-5xyz)cos(15z) Find ôxôz

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Q: 4. J (cos x – sin x)²dx

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Q: S-) Find the general soluhon of sin'x y"-(25inx.cos x)y'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Please check step 2 for solution

Q: 7) Suppose cos(x – y) = xy. Find at the following points 7.1) (0, 5) 7.2) (0,– 5)

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Q: . Let z = 1+ cos 0 + i sin 0, where - < 0 <0. (a) Show that |z| = 2 cos -1 and arg z = (b) Hence…

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Q: 9. For each n E IN, let Xn be the set of polynomials of degree equal to n, and let Pn = U_0 Xk. True…

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Q: 18.8. (a). Let y be the contour z = ete, - T<0< T traversed in the positive direction. Show that,…

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Q: Q2. Evaluate $. dz where C is: (z2+1) cosnz Ay 3/2 1. Iz – 2i| = 0.5 2. %3D -1 1 x |-1/2

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Q: Q.3) Evaluate the following dx 1) [ x² + 10x + 30 T 2) [²√³x² 3) ² ² 1/2 dx xy y sin x dx dy dx dy

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Q: 18.) Suppose x = R cos(0) sin($), y = R sin(0) sin($) and z = x² + y? + z? = R²Y R cos(). Verify the…

A: Given

Q: 1. Given : R]-1 GJ Cos20 Sin20 2sine coso sin20 Coso -2sin& cost |-sintcost Sint cost Cos-Sine Prove…

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Q: 1.4 The integral 2 sin (15ax) sin (10a.x) dx equals: (a) (cos (5ax) – cos (25ax)) da (b) (sin (5ax)…

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Q: If y = exp(-x²) show that = -2xy and hence prove that, for n > 1, y(n+1) + 2xy(") + 2ny(n-1) = 0.…

A: Given that : y=e-x2. Therefore,  dydx=ddxe-x2=e-x2.-2x=-2xy  , as y=e-x2. Hence proved that…

Q: 6.(5.2) For R[0,1] × [0, 1] evaluate the following. (1) I I: = SSP (xy)2 cos(x³) dx dy R (2) 1 =…

A: Step 1: Solution-(1)Given: For R=[0,1]×[0,1] I=∫∫R​(xy)2cos(x3)dxdyOur aim is to evaluate the given…

Q: o find for: y = sin(x") + 2* +n

A: Given,          y=sinxx+2x+π

Q: 1. Show that f(r) = sin(r + 3r) is equal to g(r) = -I Cos(I) at least once on -l. Hint: Think about…

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Q: 12. y = cose. y=taro +√3 find cartesian tion. едиа O lin) find I = /₁13 (1+ x³) dy

A: To find the Cartesian form.

Q: sin ydy (4 + cos y)²/3

A: We know that integration of xn is xn+1/n+1 +C. Here C is integral cosntant.       Here i attached…