tanode B В sec®

Q: Evaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the curve C: a = 8 cos t, y = 16 sin t (0…

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Q: Problem 8 Find the following indefinite integrals: (a) [3r°dr (b) S(3r® +9x² – 12r)dr (c) S(7x-1…

A: topic- indefinite integral ∫xndx=xn+1n+1+C

Q: X= 6 The area enclosed by the curves Y= and y= 2x from x= 1 to x= e is 2) e +1 O 3) +1 O 4) 2-2

A: Given query is to find the area enclosed by the curves.

Q: Evaluate the integral directly by integration with respect to x and y. 4 x= (y/4)+ 1 4x - y -dxdy 4…

A: We have to find the value of the double integral ∫04∫x=y4x=y4+14x-y4dxdy Since dx present first in…

Q: 422+3r-2 Given z+1 determine y" 18 (z+1) (z+1) 2 (z+1) 10 (z+1)

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Q: 3. For the given differential equation xy' – 4y = x*e* a) Find P(x) and Q(x) functions of a FOLDE.…

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Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: Find div F and curl F if F(x, y, z) = 11y"2°i – 17x"z1ºj – 6xy°k. - div F= curl F=

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Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

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Q: (- 1)"(x + 1)" n! Consider the series E n=0 (a) Find the series' radius and interval of convergence.…

A: We will use Ratio Test for convergence

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 12x) dx Cos In x +…

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Q: f(x) z400 g(x) lim where f(r) and g(x) are seen in the graph. 3 S(x) 2 -5 -4 -3 -2 -1, 2 9(x)

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Q: evaluate y" -2y' +5y=0 y(0) =1, y'(0)=3

A: Solve the following

Q: The astroid curve below is defined by the parametric equations x(t) = 2 cos' t, y(t) =2sin't.…

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Q: Ay 4- 2- -> 4 -2-

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Q: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

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Q: Find V· (V × F) if F(x, y, z) = 9 sin xi + 5 cos(2x – 3y)j+ 7zk. - V·(V × F) %3D

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Q: 4 Determine the set of x-values where f(x) 12z is continuous, using interval notation. (-x,5) u (…

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Q: Let e, = ( ) be a unit radial vector, where r = Vx? + y + z?. = (1 (a) Calculate the integral of F =…

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Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A: Given problem:- Find the conservative vector field for the potential function by finding its…

Q: 21 Given 3x7 +8x5 - , determine, y" O 630x4 + 480x² + 126 5x4 O 840x3 + 360x 504 - 504 O 2520x3 +…

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Q: Find the series' radius of convergence. n! Σ 5-10 - 15...- -5n n= 1

A: We have to find the radius of convergence.

Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

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Q: Solve the initial value problem. 4 y(x) = 4 sec(3.xr) tan(3x) ; y(7) = 3

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Q: Find dy/dx. x = Vt y = 9-t dy dx

A: Here, x=t3y=9-t

Q: Evaluate. 1 6 x dx V16 +3x2 0. V19 A) B) 2/19 -8 C) V19 -4 - 2 D) -219 +8

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Q: The company can sell the item for $90,000 each. a) Write a cost function C(x) and a revenue function…

A: Given query is to find cost function, revenue function and profit function.

Q: The acceleration function (in m/s2) and the initial velocity v(0) (in m/s) are given for a particle…

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Q: dx x² + 4

A: A detailed solution is given below.

Q: Find f and f, and evaluate each at the given point. 3xy f(x, y) = V2x + 2y (1, 1) " (x, y) = 5,(x,…

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Q: Question 4 Determine the derivative of the given function: y = (e + e*)3 Oy = 3(e+e) (e" - e) Oy =…

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Q: Find dy/dx. x = Vt y = 9-t %3D dy dx

A: The objective of the question is find dy/dx.

Q: Q2/ Check the symmetry of r² = -sin(20) %3D Ans./ Symmetry about the origin

A: Symmetry

Q: Find the particular solution determined by the given condition. F(x) = 3x2 - 2x; f(O) = 9 %3D %3D O…

A: Given query is to find the solution of the differential equation.

Q: Find curl (7z i + 8x j+4y k).

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Q: 10 8 10 If f (x) dx=17 and f (x) dx=12, then f (x) dx =5. (A) True B) False

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Q: Determine if the function is a solution to the given differential equation. y = x In x + 6x + 5; y"…

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Q: Solve the problem. dV The growth rate of a certain stock is modeled by = k(25 - V), V = 20 when t=…

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Q: Represent the following equations in R? by a vector-valued functions. Imet gaoglecomis shwing your n…

A: Given

Q: The derivative with respect to x of (3i-1)ar is 3-1 by the 2nd fundamental theorem of Calculus A…

A: let f(x) =∫3x ( 3t-1) dt

Q: Solve the differential equation for general solution 7y6dy = 8x

A: Given query is to find the solution of the differential equation.

Q: If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f{g(x)}…

A: If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f{g(x)}…

Q: Problem 3 Use the rules of differentiation to to find the derivatives of the function: (a) f(r)= 3rª…

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Q: A spring with a natural length of 10 cm, is stretched by ½ cm by a 12 N force. Find the work done in…

A: Given query is to find the work done .

Q: dr 5. 2 ?+3 2

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Q: Evaluate the line integral | -ydx + xdy along the curve C : y? = 18x from (18, 18) to (0,0). NOTE:…

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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Q: about the line, x- | (E'1) puo (!!)'(0) squiad %3D V= T RG) 3-X y= 2x+1 Idy 3 - 23. x- V= T 29 12

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Q: The partial derivative of f(x, y) = e"y – 2x – 4y + 3 with respect to x is O ye"V – 2 af af ery + y…

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