:-Solve the following equations (choose three only):- 2 1- y' + ²y = -x³y5 2- 2xydx + (x²-1)dy = 0 3- x²y + 3xy' + y = 0 d²y dy 4- 4 + 5y = sin3x - dx² dx 5- 2xy' + 2y + 8x³

Q: What are the cylindrical coordinates of the point whose spherical coordinates are (3, 5, 1)? r = 0 =…

A: Given: spherical coordinates ρ,θ,φ, here ρ=3,θ=5φ=π6 To find : cylindrical coordinates r, θ, z

Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t) ||³ = r(t) = e³ti + e-tj to find k(t).

A: By using the formula kt=r't×r''tr't3 to find kt.rt=e3t i+e-t j

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Q: Homework 11 Parametric: Problem 2 Eliminate the parameter t to find a Cartesian equation for: and…

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Q: If f(3) = 11 and f '(x) ≥ 3 for 3 ≤ x ≤ 7, how small can f(7) possibly be?

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Q: Which of the following is the derivative of (x³ + 1)(x² + 2x)? 3x²(x² + 2x) + (x³ + 1)(2x + 2) 3x²…

A: This question is based on product rule of differentiation.

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Q: Sketch the region enclosed by the curves x − 5 = 4y and x − 21 = (y – 4)², and compute its area. A

A: The given curves are; x-5=4y and x-21=y-42 Now find the point of intersection between the given…

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: p(x), χ b on [a, b], which of the following is/are In f(x) continuous always true?

A: Given that q(x) is  continuous on [ a , b ]  which means f(x) is continuous on [ a , b ] .       as…

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A: Work done on particles: W = F.dr

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: To find the domain of the following vector‐valued function.rt=25-t2 i+t2 j-4t k

Q: Ex. (7) Sol:- Solve y" +y'+y=6sin (2x) ➤ For y y"+y' + y = 0 Homogeneous [6sin (2x)=0] m² +m+1=0 1…

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Q: Which of the following is the derivative of x³ + 4x + 1? x² + 4x 3x² + 4 x²+4 3x²+4+1 3x² O

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Q: 2. Find the area between the curve y=-x and y+x²= 2x.

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Q: Evaluate the line integral. [(x - y) ds C: x² + y² = 16 Lox (x - y) ds = C i

A: Evualate the line integral

Q: Evaluate the definite integral. 15t L² (elst i + e i+e¹j+t k dt 1 k)di

A: Here we have to use the concept of definite integral.

Q: Find the area of the region between the curves y = x and y = √x. Area between curves =

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Q: Evaluate F. dr along the line segment C from P to Q. F = -7xj; P(8, 3), Q(8, 4) #1 [F F. dr = i

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Q: Using the Mean Value Theorem In Exercises 13-18, determine whether the Mean Value Theorem can be…

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Q: y" - y'-12y=6sin (2x)

A: Given problem:- Solve y'' -y' -12y= 6sin(2x)

Q: Find the limit. NOTE: Enter the answer using round brackets. t² +1 1 lim t +∞ (?, ?) 6t² + 7' 3t ||

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Q: d d Calculate[ri(t) r2(t)] and[ri(t) r2(t)] first by differentiating dt the product directly and…

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A: Given that      f(x) = x3

Q: Prove the identity. COS X 1-sin x 1+ sin x COS X Note that each Statement must be based on a Rule…

A: Solution )  cos x / ( 1 - sin x ) Multiply cos x in numerator and denominator =cos x × cos x /  […

Q: ind r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). r(t) = 2t²i - 2tj + 5t³k (a) r'(t) (b) r"(t) (c)…

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Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = e, y = 1…

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Q: Write the given (total) area as an integral. • The area above the x − axis and below y = 4 − x²

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Q: lim x++∞ COS X log logi x

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: 11.7 Triple Integrals OPEN Turned in automatically when due. 4. Practice similar Help me with this…

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Q: onsider the quadratic function f(x) 2²-3x + 10. etermine the following: (enter all numerical answers…

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Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6 P6(x) =

A: nth Maclaurin polynomial for the function :       Pn(x) =  ∑i=0n fi(0)i!xi = f(0)+f'(0)x + f''(0)…

Q: Find DO NOT SIMPLIFY YOUR ANSWERS. 1. log √2x² + y + 2x² + y) + tan(x™ — ñ³) = sin¯^¹²(x² − 1) + ½ /

A: To dydx.log32x23+y+tanxπ-πy=sin-1x2-1+π2

Q: r(t) = 2ti - 2tj + 시 6 t³k

A: Given :

Q: the solids generated by revolving the region bounded by the graphs of the equations about the given…

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