Find f such that f'(x) = f(x)= f(16) = 21.

Q: Evaluate the following double integral over the given region R. 2 ln(x + 1) (x+1)y Use integration…

A: The objective of the question is evaluate the definite double integral.

Q: 4. x = 3 + 4 sine, y = 3cos0 - 4

A: Given: x=3+4sinθ, y=3cosθ-4 dxdθ=ddθ3+4sinθ = 4cosθ dydθ=ddθ3cosθ-4 = -3sinθ

Q: terval of convergence of the series Σ(√n+1-√n)(x+2)" is given by -3<x<-1.

A: It is convergent when  |x+2|&lt;1  -1&lt;x+2&lt;1  -3&lt;x&lt;-1

Q: The cylindrical shell method is to be used to compute the volume of the solid generate by revolving…

A: Solution is here

Q: Find the area of the plane region bounded by y=-x+2 and y= x2 −2x 7 s.u. 9 S.U. S.U. 9 s.u.

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Q: Given the function f(x, y, z) = x ln(1 - z) + and simplify your answers. a) fa b) fxz sin(x - 1) 2y…

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Q: Find the solution of y" − 8y' + 16y = 0, y(0) = 1 and y'(0) = 5. y(t) = Ae4t + Be-4t y(t) = e4t+te4t…

A: The given equation is;  y''-8y'+16y=0, y(0)=1 and y'(0)=5.

Q: Part III: Equation Conversions 4 1. Convert r= into a rectangular equation. 2-sine 2. Convert 2x -…

A: Topic:-  polar and rectangular coordinate system

Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³ + 1| + C dx…

A: The integration of the integral is 1/[x^(1/3)+x^(1/2)].

Q: D. Graph each of the given functions and solve for the area of the region that they enclose. 1. f(x)…

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Q: f ƒ (a,b, c) = cos (ab) + sin (b) + c where ƒ ((2, 73,7)) Evaluate af да (1,3,7) O Option 3 T√3 12 ل…

A: Topic:- application of partial derivatives

Q: (a-x)² (a-y)² (a-z)² Express (b-x)² (b-y)² (b-z)² as a product of two determinants and hence…

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Q: If u = eª₁x+₂y+a, where a₁, a2, a3 are constants and 2² u J² u 2² u + = U. a² + a² + a² = 1. Show…

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Q: For a cyclic group of order 420, the number of generators are, (a) 66 (b) 76 (c) 86 (d) 96

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Q: 1- f(t) = 2t³; 3–f(t)=sinh(2t); 5-cosh (t) sin(2t);

A: Given :1. f(t)=2t33. f(t)=sinh(2t)5. cosh(t).sin(2t)

Q: The integral can be rewritten as 6u³ (a). Joudu u+1 6u4 (c). du u²+1 ܐ | dx √x+√x (b). Sū 6u² u²+1…

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Q: find the surface area of the portion of the curve x²+y²=4 from x=0 to x=2 when it is revolved about…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. The x-coordinate of the centroid of the…

A: Solution is given below:

Q: create 2 sample word problems of chain rule

A: 1) Differentiate cos(sin(ax)) by using chain rule   d/dx { cos(sin(ax)) }  =  - sin(sin(ax)) * {…

Q: Let y = = 1/2 √ √x. Then evx dy dx is:

A:

Q: Classify the following differential equation: Second order, nonlinear Nonlinear, homogeneous Linear,…

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Q: A B Ⓒ 1 D 2 E 3 3 4 3 ["/* sect sec*x dx

A: The integration of the integral is sec4x limit from 0 to pi/4.

Q: Given the function f(x, y, z) = x ln(1 − z) + following and simplify your answers. a) | fx b) u fxz…

A: We can answer both the answer as below

Q: stion 12 The power series representation of f(x) = ln(x²-1) is given by OA. None of the choices in…

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Q: -3x² 2(T T + 10 25)

A: Follow the procedure given below.

Q: Show that if the function f(x, y) = ecos-e-cosx, satisfies Laplace Equation.

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Q: Find two numbers whose sum is a, if the product of the square of one by the cube of the other is to…

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Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² - 4 = 0, using a vertical element. A…

A: Using vertical element form a double integral then solve it

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. The y-coordinate of the centroid of the…

A: We first sketch the given region using a graphing calculator.  We will consider the graphs about…

Q: Given the partial decomposition of the rational function for some numbers A, B and C. What is the…

A: Given :x+1(x-1)(x-2)(x+3)=Ax-1+Bx-2+Cx+3

Q: If R is the disc with center at the origin and radius 5 then the numerical value of [xdA is equal to…

A: Please follow the next step.

Q: 2-f(t)=3e-²¹. 4-f(t)=2 cos(3t). 6-f(t)=cos't-

A: Answer highlighted 3 questions(2,4,6)

Q: fx ln x dx.

A:

Q: The value of x for which the series - OA25x<3 or 3<x≤ 4. OBx<2 or 4<x. OC. None of the choices in…

A: We will solve this question by first calculating the radius of convergence of the series.

Q: The cylindrical shell method is to be used to compute for the volume of the solid generated by…

A:

Q: $(2xy - x²) dx + (x+y²)dy, where C is the enclosed curve of the region boundec. The value of by y=x²…

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Q: The height and radius, respectively, of a cylindrical tank is 5 m and 2 m. If the tank is full of…

A: Given that: Height = 5 m Radius = 2 m We take a slice of height △x at a height x So the volume of…

Q: The graph of r cos 0 + 4 = 0 is symmetric with respect to the no symmetry Oy-axis x-axis O origin

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Q: IV.Sketch the ff. curves: Find all its properties. X 1. y= In x

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Q: Draw the graph of y = 3x2 + 6x − 24 and label its minimum

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Q: A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The…

A: Solution is here

Q: Which of the following integrals represents the area inside the curve r = 3 + 2 cos 0 and outside…

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Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

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Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³+1| + C dx…

A: To evaluate: ∫dxx3+x Let I = ∫dxx3+x Assuming x=u6⇒dx = 6u5du

Q: h-x'+2x=10e³ where x(0)=6

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Q: - Find the value of x of which the function f(x) = O a. none of these O b. 1 OC -1 O d. -3 Oe. 3 2-8…

A: Given:f(x)=12x-8

Q: 2. Consider the spherical equation given by p = 4 cos 0 sino. Determine its corre- sponding equation…

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Q: Find the value of (D) solve in detail 1219 = 20.88 * (0.015/60)1.85 4.87 D4 Ans. D= 0.0186

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Q: Evaluate the following double integral over the given region R. JS Ta 4 ln(y + 1) (x + 1)(y + 1) dA…

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Q: Consider the series Σ(-1)^ 2³ Which ONE of the following statements is CORRECT? n=1 3" OA. The…

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