(10 sin(x-sin(x-dx 6 2 (Ans: - sin(2x-2) + 5 x + C)

Q: Evaluate the surface integral s G(r) dA, G(r) = x+y+z, S: z=2x-y, 0 ≤ y ≤ 1, 0 ≤ x ≤ y

A: Given:    Gr=x+y+z,    S: z=2x-y       0≤y≤1, 0≤x≤y Substitute z=2x-y in Gr     Gr=x+y+2x-y…

Q: Calculate the indicated Riemann sum Sn​, for the function ​f(x)=x2−9x−4. Partition [1,7] into six…

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Q: Given: f(t) = 8 sin23t. Evaluate: F(1) Use 2 decimal places.

A: f(t) = 8 sin23t.

Q: Find div F if F(x, y, z) = (x² + y)i + z² j + (ey - z) k. O 2x - 1 O 2xy - 1 O 2xi-k O 2xy i+ k

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Q: 1 For r(t) = − i − j + m(1) k - j + ln(t)k and u(t) = t²i − 2tj + k. t d Find [r(1) · u(1)] ²3 +…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: inverse laplace transform

Q: Given: F(s) = (2s+3)/(s² -2s +5). Evaluate: f(1) Use 2 decimal places. 5.67

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Q: Determine whether the differential equation is exact. If it is exact, find the solution. (7x² − 2xy…

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Q: Classify the given differential equation according to its type, order, degree, and linearity. d²y…

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Q: The marginal average cost of producing x digital sports watches is given by the function C'(x),…

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Q: 5. L Evaluate [F DETAILS F. dr. LARCALC11 15.2.029. F(x, y) = xi + yj C: r(t) = (5t + 8)i + tj, 0…

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Q: Given f''(x)= Find f ƒ(7) = = 1 25 sin(5x) and f'(0) = 5 and f(0) = -6.

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Q: (a) ах = Du DE = du, ada voa waye by oz + + + 2x DE 2. (x²= y² + x) x (2x+₁) + (-2xy-9)x (-2y) (2x +…

A: We have to simplify (x2 - y2 + x) × (2x + 1) + (-2xy - y) × (-2y)

Q: = (2x²-3x+1 2x-1 ,x 0.5 Determine constants A and B such that is continu values of x. Show your…

A: Topic:- application of calculus

Q: 1. Calculate the following unknown quantities. (a) P= (kx 1000), r= 1.2%, t= Find S.

A: As per the rules we can answer only first question and rest can be reposted.

Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

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Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

A: here the given differential equation  (6 -20y +e-5x)dx -4dy = 0 this can be written as  dy/dx +(5)y…

Q: Which of the following represents the graph of (x + 2)² = 4y - 6)? O -83 4 ry 14 11 10 9 8 " 5 4 3 2…

A: The given function is x+22=-4y-6

Q: If My - N N equation = Q, where is a function of a only, then the differential has an integrating…

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Q: y' = 4+t-y, y(0) = 1 (a) Find approximate values of the solution of the given initial value problem…

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Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: Determine the smallest degree of the Maclaurin polynomial required for the error in the…

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Q: Which is the focus and directrix of the parabola with equation (y + 0.5)² = 4(x - 1)? Focus…

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Q: Find the solution of the given initial value problem. ty' + 2y = sint, y(7) = 5, t > 0 y = cos(t)…

A: As we know that; The standard of the First order linear differential equation is: dydt+Py=Q Where, P…

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: V. (VXF) =

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Q: Show that the sequence defined by 1 a₁ = 1 an is increasing and an < 3 for all n. Deduce that {an}…

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Q: If N₂- My M equation = Q, where Q is a function of y only, then the differential M + Ny' = 0 has an…

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Q: Given: F(s) = (5s+6)/(s²+9). Evaluate: f(1)

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Q: 13. +27x-27 √x² dx √x² - 6x +9 2 (Ans: x³ + x² + 36x + 81ln|x − 3| + C)

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Q: ind V. (V × F), if F(x, y, z) = = V. (V X F) = ezi+ 6xe¹j - 3ek.

A: Topic:- vector algebra

Q: For question 1c, the final equation is x-2y+1=0

A: We have to eliminating parameter t  (C) x = cos(2t),  y = cos2(t)

Q: The area under one arch of y=sin(0.5x) is O 0.2 O 0.5 O 0.8 None of them

A: Given: y=sin(0.5x)

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Our Aim is to find the inverse Laplace Transform of the following function given…

Q: hraj h(x) = 3x-2 x347

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Q: II. Consider the function f(x, y) defined for all (x, y) by ƒ(x, y) = 232/32 + 2xy + 4x²y (a) Find…

A: Here we have to find the critical points.

Q: 6 5 4 3 a The function graphed above is: Increasing on the interval(s) Decreasing on the interval(s)

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Q: Find the curvature and the radius of curvature at the stated point ㅠ r(t) = 11 cos(t)i + 10 sin(t)j…

A: The expression for the curvature is: κ=r't×r''tr't3 And The expression for the radius of the…

Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: Find curl curl (5z i + 6x j + 8y k) i 5 i i 6 (5z i + 6x j + 8y k). 8 = ( )i + ( )j + ( )k

A: Given that a vector 5z i^ + 6x j^ +8y k^ We have to find a curl of this given vector. Curl of a…

Q: Find the limit lim x →∞ √1+ 2x + 9x² -2x + 5

A: This question is related to limits, we will solve it using given information.

Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: Here, the diameter of the hemisphere is 30 m. So, the radius of the hemisphere is: r=302=15m=1500 cm…

Q: Fill in the blank. (Enter your answer in terms of t.) 1 * ¹{2 ² - S 2

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Q: 4. Choose a solution to the differential equation y" + 3y' + 2y = sin eº. -2x -2x cos €² e + e е -2…

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Q: Find the domain of the vector-valued function. r(t) = n(t) 0 (-∞, +∞0) O (1, + ∞ ) O (0, +∞ ) O [1,…

A: Find the domain for all three components and then take intersection of those.

Q: Find the derivative of the function. f(x) = arcsec(4x) f'(x) = 4 4π√ 16x² - 1 :or 1 xV 16x²-1 2

A: Topic = Derivative

Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

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Q: S √√x+12 X S- dx using substitution. √√x+12 c. Verify that your answers to parts (a) and (b) are…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r = 4 cos 0 -…

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Q: Which is the center and radius of the circle given by the equation, x² + y² - 6x 10y + 11 = 0?

A: The answer as follows: