Find the curl of the vector field F(x, y, z)= e sin yi - e cos yj.

Q: Find an equation of the plane containing the point P (1, -7,1) and the line r (t ) = .

A: Given: The point P (1, -7,1) and the line r (t ) = <3 − 2t, 4t, 7> . So,             x = 3 −…

Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: fxsinxdx O xcos(x) -In sin(x) + C ○ -xcos(x) + sin(x) + C O xcos(x) + sin(x) + C O xcos(x) - sin(x)…

A: Topic = Integration

Q: ƒ cos(x³) x² dx. 1 ¹ cos4 + c 4 1 WIT 3 1 -| sin x³+ C 1 ·cosª + c 4 4 -3 sin x³+ C

A: Topic = Integration

Q: 2x3 2x² + 3 3 Submit an exact answer using fractions if needed. Find the average value of f(x)…

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Q: Sxex² dx O 2+x²²/²/2/ HI HIN 6 1 2 HIN ex²+ + C + C + C

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Q: da Find at z = 4 if y = 4z² - 1 and dt da dt 11 > Next Question dy dt = -5. 11

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Q: n=1 n²2n-1 (-5)n

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Q: Let f(x) = |x-1 (a) Make tables of the values of f at values of x that approach x = -1 from above…

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Q: ["[" f(2,3) dy dr True False [1 f(x, y) de dy

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Q: s After an appropriate trigonometric substitution, the integral transformed into which one of the…

A: Concept: The trigonometric change: The trigonometric identities can be used to assess several…

Q: Find the Maclaurin Series representation of the function f(x) = x cos(2x). (Hint: If you know the…

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Q: What region R in the ry-plane minimizes the value of the following expression? f (x² + y² - 9) dA R…

A: The given double integral ∫∫Rx2+y2-9dA we have to find the region R on the  xy-plane that minimize…

Q: 23. The distance from a point (2, y) to the line 4x + 3y =0 is equal to 5. Find the value of y. O…

A: Given that the distance from a point 2,y to the line 4x+3y=0 isequal to 5. We need to find the value…

Q: Question 3 A dilution tank initially contained 100L of fresh water. Then water which contained…

A: As per our guidelines answer first three subpart of a multipart question. So please resubmit the…

Q: 8. Consider the differential equation e* (y - x) dx + (1 + e*) dy = 0. (a) Show that this is an…

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Q: The marginal cost for printing a paperback book at a small publishing company is c(p) = $0.016 per…

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Q: Find an equation of the plane. the plane through the origin and the points (4, -5, 2) and (1, 1, 1)

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Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

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Q: Express the following endpoint sum in sigma notation but do not evaluate them L10 for f(x)=square…

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Q: Evaluate the following integral using integration by parts. 4x sin 4x sin x cos x dx Let u=4x sin x.…

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Q: Find a and b such that ƒ(x) = x² + ax + b 8 17 has an average value of 933 over [0,1] and an average…

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Q: Find the equation for ​(a) the tangent plane and ​(b) the normal line at the point P0(1/2,1,e) on…

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Q: 1- Maryam sits at the point on the curve y=(×+2)? where the normal to that curve is parallel to the…

A: 1st question's answer: If Maryam sits at the point on the curve y=x+2, then it's normal won't be…

Q: Set up a triple integral using cylindrical coordinates that finds the volume of the solid bounded…

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Q: Find the general solution to the differential equation: y' = 8x + e²r

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Q: a) z=x²ln (x y²) b) z=4 cos(x-3y)

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Q: [sin¹ 3x cos² 3xdx

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Q: Question Find the change in surface area dA if the radius of a sphere changes from 11 cm to 10.8 cm.…

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Q: Suppose the demand for a product is given by D(p) = A) Calculate the elasticity of demand at a price…

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Q: The power series xn What is the power n! series representation of e(-²) ? ex is n=0 n=0 n=0 None of…

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Q: Consider the function f(x) = 2x³ 12x² 30x + 7 on the interval [-4, 7]. Find the average or mean…

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Q: and f(a) f(x) = 4x² + 5x² + 6x-7 3 7 2. Find f(x), f"(0), given

A: Given a function f(x)=4x3+5x2+6x-7 We have to the following of the given function, f''(x) f''(0)…

Q: 2. Let f(x) = 2x²-3x+1 ,x 0.5 Determine constants A and B such that is continuous for all values of…

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Q: Question Find the change in volume dV if a circular cylinder with radius r = 8 changes height from 7…

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Q: Find the area enclosed by the polar r = 2 (1+sine) Curve

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Q: = 4 cost, Use an integral to find the area of the region bounded by the curve x = y=5sint, 0≤t≤2π.

A: SOLUTION-

Q: Use substitution method to evaluate the definite integral fore dx

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Q: 5. Solve the differential equation dy 4t dt y² + t²y² = subject to the initial condition y(0)=2.

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Q: *7. Draw the region whose area is given by the definite integral. S₁₁7 = dx Which graph shows the…

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Q: 1. Solve x²-3x²10x + 24-0. Show at least one long division process.

A: Let P(x)=x3- 3x2 - 10x+24 P(2)=23- 3(2)2 - 10(2)+24=8-12-20+24=32 When x=2, p(2)=0. Thus x-2 is a…

Q: ind the area between two curves f(x)=8-x² and g(x) = x².

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Q: 3x + 7 Consider the function f(x) = 4x + 1 and (A, ∞o) where the function is not defined at A. Find…

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Q: Question Find the average value of f(x) over the interval [0, 2]. Submit an exact answer using…

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Q: Estimate the area under the graph of f(x) = rectangles and right endpoints. Rn = Repeat the…

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Q: If the series un is convergent, n=1 then the series (−1)ª un is also convergent. n=1

A: Given first statement is true and second statement is false.

Q: (1 + y²) dx + (x²y + y) dy = 0.

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Q: Question 2 (a) Find, by completing the square, the inverse Laplace transform of S+5 s² +8s+21 (b)…

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Q: Express -2√3 - 2i in the form ree with 0 ≤ 0 < 2π. O 4ei O 4e¹ 4ei 5m 4e 6 11 m 4e 6 2

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Q: (1 + y²) dx + (x²y + y) dy = 0.

A: The differential equation is given by 1+y2dx+x2y+ydy = 0                               ........1 To…