Evaluate [ f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: z = x + y, x² + y² ≤ 1

Q: 2. Solve the differential equation dx for y = f(x) with the initial condition y(0) = 2.

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Q: 4. Consider the vector a=(-2,3,-1). [ [K/U] Find the magnitude of the vector ä. b) Find an unit…

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Q: Solve the following (i) 33x-5- = 9/x equations: (ii) 22x+2 = 42x-1

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Q: Write the sum using sigma notation. 1² +2²+ 3² + +9² K Σ Need Help?

A: To write the sum using the Sigma notation.

Q: Find the second derivative of the vector-valued function r(t) = (4t+ 3 sin(t))i + (5t + 3 cos (t))…

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Q: In the below series find the missing noumber  2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

A: Given data:- The below series is given, 2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

Q: Let f(x) = 2log₁(x) f'(x)= ƒ' (6) =

A: We have to solve above question

Q: Differentiate the following function. You do not need to simplify the derivative. dy d.x || y = 2e²²

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Q: Evaluate [(e²/² - x)(e²/² + x) dx. Show your work.

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Q: Use reference angles to evaluate sec (11"). 3 Enter the exact answers. For the number 7, either…

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Q: Differentiate the following function. You do not need to simplify the derivative. 3x²e10r g'(x) =…

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Q: Given f''(x) = 7x - 2 and f'(0) 2 and f(0) = 1. Find f'(x): and find f(4) =

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Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

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Q: əz 7. Find the partial derivatives and if: əz əx ду (a) z = x-y r2 + 1² (x, y) = (0,0) = x² sin(x-y)…

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Q: Find the area of region A in the figure if the equation of the boudary is r = 4 cos (0). r=1 A A = X…

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Q: Find d dr (73 (7²). Type In(x) for the natural logarithm function.

A: As we know that; The Power law: ddxxn=nxn-1 And the common derivative; ddxlnx=1x   Let, y=7x

Q: Devin invested an amount of $10,000.00 in a mutual fund. After 2 years and 6 months the accumulated…

A: The solution is given below

Q: A lamp post 3m high is 6m from a wall. A man 2m tall is walking directly from  the post toward the…

A: Given:- The given lamp post 3m high is 6m from a wall The given man's height is 2m The man is…

Q: Find (3x + y)dA where D = {(x, y) | x² + y² ≤ 16, z ≥ 0} Round your answer to four decimal places.

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Q: Consider points A(4, -1, 3), B(3, 1, 6), and C(1, -3, -3). (a) Find the area of parallelogram ABCD…

A: The given problem is solved below in detail.

Q: Find the average value of the following function where 9 ≤ x ≤ 11: f(x) = X C 81 dx

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Q: How long will it take for an investment of $3000 to double in value if the interest rate is 6.5% per…

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Q: Find the arc length (s) of the curve r(t) = (est, -2e5t, 3e5t) for 0 ≤ t ≤ In (2) 8=

A: The arc length s of the curve r→t=x(t), y(t), z(t) for a≤t≤b is given by s = ∫abx'(t)2+y'(t)2+z'(t)2…

Q: You are taking a road trip in a car without A/C. The temperture in the car is 105 degrees F. You buy…

A: Above question is solved.

Q: J 9(x, y, z) dV over solid B. B = {(x, y, z) | x² + y² ≤ 9², x ≥ 0, y ≥ 0,0 ≤ z ≤ 4} and g(x, y, z)…

A: Please see the below picture for detailed solution.

Q: Find the particular solution of the following second order differential equation d² y dy dx² --4-…

A: The given differential equation is :d2ydx2-4dydx-21y=-105x-209given that y0=11 ; y'0=39.

Q: Solve the differential equation (3x² - 2y²) y' = 2xy; y (0) = -1 O a. y² = 2x²(x + 1) O b. x² =…

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Q: Find the domain of the vector function r(t) = Domain: {t |} ≤t≤

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Q: Evaluate the following indefinite integral. 1 √2 + 3x² Note: Don't forget your C! And be sure to use…

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Q: Solve the differential equation xdæ +sin? (%) [yda — xdy]=0 2x a. 4x In 2y + x sin (2²) = 0 O b. 4x…

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Q: Compute the given integral. fcos¹ a a sin ædx = +C

A: Our Aim is to evaluate the integral given below:-∫cos7 (x) sin (x) dx -(i)

Q: Find the indicated value. f(5,2) if f(x,y)=2x²y-5xy³ f (5,2)= 10 (Type an integer or a simplified…

A: Given a function fx,y=2x2y-5xy3 We have find the value of fx5,2 Derivative of a polynomial function…

Q: 2 1 Expand 2y 0.013 2 3. ✓0.0004:

A: Given problem:- Expand 2y210.013y2230.0004

Q: Differentiate the following function. You do not need to simplify the derivative. dy dx || y = 2e²²

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Q: 2x lim(x,y)→(0,0) x² + x + y²

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Q: Find the tangent plane to the equation z = - 3x² + 2y² + 4y at the point (4, 1, - 42). 2 = Check…

A: I am attaching image so that you understand each and every step.

Q: Given the differential equation dy dx = y³ x ex² 9. Find a solution that satisfies the initial…

A: Differential equation: dydx=y3xex2

Q: Evaluate the indefinite integral. 5 fz¹ √8+zºdz + C

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Q: Find the radius of convergence for: (-1)"x" √n +7 n=1

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Q: Let f be the function graphed below. If 20 subintervals of equal length are used, write a summation…

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Q: Which function has Maclaurin series (-1)"2""? n:o OAI OB 8. 2/7/2 Oc O D. TIZE D.E. 2

A: The given series: ∑n=0∞-1n2nxn

Q: Find the exact value of sin (77) 3 sin T 3

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Q: Find the arc length (s) of the curve (t) 8 = r(t) = (5e³t, 4e³t, 2e³t) for 0 ≤ t ≤ ln(4)

A: The arc length s of a curve r→t = xt, yt, zt for a≤t≤b is given by s = ∫abx't2+y't2+z't2 dt

Q: a) Use the Newton-Raphson method to solve the following equation for x to six decim x - ln x=8 (Use…

A: Here we have to use the Newton's raphson method

Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

Q: Find the cross product u x 7 where u = 2i -3j +k and = (7, - 3, 4). ü xü= Check Answer

A: We have u→=2i-3j+kor u→=2, -3, 1Alsov→=7, -3, 4

Q: 1. Determine if the following limits exist: (a) (a) lim (x,y)→(0,0) lim (x,y)→(0,0) ₂2 x² + y² 1 —…

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Q: √√√x- S: z 12, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

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Q: Evaluate the integral: (A) Which trig substitution is correct for this integral? 1 0x = -sec (0) 10…

A: The given integral is: ∫dx64-10x232 (B) To find: Which integral do you obtain after substituting for…

Q: 5. The population, P, of an island, y years after colonization is given by the function P = a. What…

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