Q4: Evaluate the surface area of the object obtained by rotating 1+ 1² dx x = √√√y +5, √5 ≤x≤ 3, about the y-axis using: ds = divergent. If

Q: dx (x+1)Vx²+2x

A:

Q: Find the value of df-/dx at x = f(a). 26) f(x) = 4x2, x 2 0, a = 2 4) I 16 3 B) 32 C) 16 D)

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Q: n (p hix ( %3D what is the dependent vaniable in

A: Solution

Q: -3 -4 Evaluate: ₂₁ (4x²y - z³) dz dy dx

A: ∫03∫-24∫10(4x2y-z3) dz dy dx

Q: Calculate using polar coordinates: 1-x² x. y. √ x²+y² dy dx So So

A:

Q: F x+y°-4xy=0 Find dy lelx su

A: Using product rule of differentiation,

Q: Compute : csc(e) d Csc evx dx CSC - Csc cot evx А. 2/x B. csc cot(evF).eF . — cSC Cot csc · cot 2 D.…

A:

Q: Find the extremum of f(x,y) = 9x2y² +4y² + 4x². %3D Answer:

A: Topic= Derivative the extremum is 0.

Q: a) [² -da rlnr b) √ JI dr √1-² arcsin x c) / 1+ Leide [" 1+424

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Q: Bonus : Show: b. f(x+c) dx fcxdx %3D ate

A: According to the Fundamental Theorem of Calculus,

Q: the extremum of f(x,y) = 7x²y² +5y² 9x?. +

A: Given that: f(x, y)=7x2y2+5y2+9x2

Q: Evaluate f (3x²y — y²)dx + (x³ - 2xy)dy, where C' is the parabola y = x²/4 from the origin to (2,1).

A: The given problem is to evaluate the given line integral of vector field over the given path C is…

Q: Find the extremum of f(x,y) = 3x²y² +5y² + 5x?. Answer:

A: Given:- f(x, y) = 3x2y2+5y2+5x2 To find:- Extremum of f(x, y)

Q: 8) Use the Trapezoidal Rule to evaluate V1+ x² dx;n = 3.

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Q: Find the extremum of f(x,y) = 7x²y2 +4y2 4x2. Answer:

A:

Q: What are the foci of(x/a)2+(y/b)2 = 1 if a<b?

A: We have the following given ellipse -  xa2 + yb2 = 1   where a<b

Q: xa, ya, + za Let A = (x² + y? + )3/2 i show that V X A = 0.

A:

Q: Use the Midpoint Rule with m = n = 2 to estimate the value for R= [0, 4] × [0, 6]. √ √ ( 3x + 2y) dA…

A: Sol:- To use the midpoint rule with m=n=2, we need to divide the rectangle R into 4 smaller…

Q: Integrate by means of substitution a) S√√4x - 7 dx =

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Q: Integrate: S dx 5+ x2 5x

A:

Q: Find lim R→∞ -R ex/6 e + 1 dx using the rectangular contour (explain in detail)

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Q: dx Evaluate using trig substitution: a x'V4-x? upo an

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Q: Find curlF for F = xyz?i+ x*yz?j+ x*y?zk.

A: Given, F→=xyz2i→+x4yz2j→+x4y2zk→ Used formulas, ∂∂xxn=nxn-1

Q: 2 Evaluate the feltowing cartesian integrats by changing them inte equivalent Pelarintegrals: ff dy…

A: As per our guidelines we can solve first question for you .You can ask the remaining questions…

Q: Coute : 2y da + 3x dy, where D is described by 0 < a < 1, 0 < y < 1.

A: We have to find the given integral. For this we can use Green's theorem

Q: Evaluate (2x – y) dx + (x + 6y) dy. C: x-axis from x = 0 to x = 3

A:

Q: - z²) – 2x + 30y = 0 da? What is the larger root from the indicial equation

A: Given differential equation, 1-x2d2ydx2-2xdydx+30y=0 Find the largest root from the indicial…

Q: ) Find the derivetine of the fnchiog h(x) = I sinhex-7x 4

A: h(x)=74sinh(2x)-7x2Differentiate w.r.t…

Q: l6X-tan 3X, (- find openint & concav f(x)= 6-(seč 3x)3 3 sec?

A:

Q: $ Find the goneral Solutim of the differen tial equatim : (D²-60 +10)y =20-e2x

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Q: Find the extremum of f(x,y) = 5x²y² +4y² + 6x². %3D Answer:

A: The given function is f(x,y)=5x2y2+4y2+6x2 .......................... (1)