Evaluate / f(z)dz when ) f(z) z+1 and y = TR (R > 0) z2 (ii) f(z) = (z+1)³ sin(z2022) and y = r(0; 1)

Q: The derivative of requires the product rule and is given by Factor the derivative of f. g'(v) = g(v)…

A: Given:Here we have given a function  .To find:The derivative of the given function using product…

Q: a3 2- Find the third derivative for = sin(÷) for f(x, y) ax3 -2sin?cos()+2 sin A:- ) sin()+3cos )…

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Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: エ+1 dx (7² +2x)

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Q: Q7/ Express in the form x +jy (1) e(r/2-j) (2) In(3 – j) (3) sin(t/4+ j2)

A: (1)  ejπ/2-j=ejπ/2-j2                =ejπ/2+1                                         j2=-1…

Q: fyx if f(x, y) = sin(xy) + x² In y cos(xy)- xysin(xy) - cos(xy) + xysin(xy) + cos(xy) – xysin(xy) +…

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Q: (1) (II) 10 F. 10 +t 10 10 -10 -10 (II) (IV) 10 10 斗t 10 t 10 -10 -10 a) y = 10e-t/2 cos 2nt b) y =…

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Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

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Q: 7. Set f(x) (a) (b) (c) (d) = 2 +4 8 cos 2x, 2sin2, + e-8/2 s² + 4 S s² +4 8 8² +4 (e) None of the…

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Q: Use the second derivative f"(x) = x(x+ 1)(x-3) to determine where the function f(x) is concave down.…

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Q: 4) Let f(x) = - ax"+1 and a x) = 4X-3 5:) f(x) = Fxan? find the 3 first f,g and h. uch that (fo gohl…

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Q: Consider the function f(x)=2 sin(). Construct the interpolation polynomial which interpolates the…

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Q: Suppose z = x + iy and f(z) = z - 1. Find w = u + iv such that f(w) = 1 + 3i (A) 3+2i (B) 3-2i (C)…

A: We have given that , fz = z - 1 , where , z = x + iy Here , w = u + iv Let , fw = 1 + 3i We need to…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = (x2 - 2x + 1) eX B) (x2…

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Q: F"(x) = 6-18x, 0) = 9, 2) = 11 F(x) = 4x -3 +Ox+9 3p3 O Tyne h

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Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

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Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

Q: show that | | J.(x)dx x² J,(x)dx = x²J¼(x) + x J,(x) – %3D

A: Apply the integration by parts method and use the identity ∫xpJp-1xdx=xpJpx, to evaluate the…

Q: (A) Evaluate / (4x – 5) (4/x + 4x) dx. x² + 3x - 6 (B) Find dy -, if y = 3 -)4 when x = 1 %3D dx

A: *we have to perform integration operation in A & differentiation operation in B.

Q: Evaluate / 3 x sin(x)dx 03 (sin(x) – x cos(x)) + c Osin(x) – x cos(x) + c 03 x sin(x) + 3 cos(x) + c…

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Q: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

Q: 5. If f (x) = (x + 1)(x2 – 2)3 then f'(x) da व्य 2= 2x (1) 2 A. & 6xx2 – 2)2 انی + (22 21 2 = Alv 3x…

A: Given query is to find the derivative of the function.

Q: 8(x) 48. f(x) 2 - x' In Exercises 51–60, show that f(g(x)) = x an dom x - 1 g(x) of 51,fx) = 2r + 1,…

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Q: se Green's Theorem to evaluate SC (5y-9x)dy-(yx-x³)dx where C is shown below

A: Follow the procedure given below.

Q: (a) (i) Use the substitution sin(u) = x + 3 to show that dx 12x + 7 -1 (x+3) V-2x² – 12x+7+c. sin -…

A: As per company guideline we are supposed to answer only one question with maximum 3 sub parts at a…

Q: MacB = (x),ƒ o (1)fp хр = (x),f o %3D (x)fp = (x),f O %3D xp = (x),f o = sin x, which of the…

A: To find the correct option.

Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: y= (12,4 + x)* + (1+)(Va² +x- c )cos²(4x), c)cos²(Ax), 3)4( 3 y = (12,4 +x)* + (1+x' Зx +x — с y = ?

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Q: 1. Let F(t) = (e¹−¹ – ť², 3t² + 1, 4-5 lnt), G(1) = (-6, 1,0), and f(t) = cost. Evaluate: (a) (F-G)…

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