Find the area in the first quadrant bounded by f(x)=4x-x^2 and the x-axis.

Q: x²-1 3. f(x) = -1;ƒ' (1) 2x+1

A: Solution is given below:

Q: 8² 8²v 8² = (x² + y² +2²) −¹, then + + is 822 მ2 If v=

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Q: 1.ƒ(x) = 4x³ – 7x² + 2x − 8 -

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Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

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Q: Let F(x, y) be a continuously differentiable vector field satisfying property problem. Show that…

A: Answer is given in next step.

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Area region = [ f(x) dx + √ [*g(x) dx…

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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: What is (x - 12)² + y² = 144 in polar form? r = 24 sin 0 r= 24 cos 0 O Option 1 r= -24 sin 0-144…

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Q: Consider the region on the 1st quadrant bounded by y = √√4x²,x and y - axes. If the region is…

A: Using shell method, given format is obtained. From this format, evaluate m-n.

Q: 2. Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal,…

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Q: If w = eb₁x-b₂y-b³z, where b₁,b2, b3 are constants and b3 + b3 + b3 = 1. Show that อพ อพ อพ 02 อ 0z2…

A: Here in this question, we need to solve the given partial differential equation. The solution can be…

Q: Hwy find the integration 3 Se vadv V 1-

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Q: (D^5-3D^4+8D^3+16D^2-9D-13)y=0 nonhomogeneous undetermined coefficients

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Q: D. Graph each of the given functions and solve for the area of the region that they enclose. 2. 4.…

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Q: Find the solution of the following initial value problem d2y/dx2 + 2 dy/dx − 3y = 12ex ,  y = 0 and…

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Q: Q2: A company plans to update its equipment so that its trucks are replaced after ten years from…

A: To find out the amount that company needs to pay each year.

Q: x^2 - 5x + 8 is equal to • 4(2x-5)^2+7 O 2(x - 5)^2-6 O (x-5)^2-9 none of the choices टट

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Q: What is the area of the region enclosed by the graph of r² = 3 + cos 0? √ √3+ cos e de √(3 + cos 0)…

A: We have to choose correct option.

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: The power series representation of f(x) = ln(x2-1) is given by Α. 24-1-1x", -1x<1 n=1 n+1 B. None of…

A: To find the power series representation of the given function.

Q: X 4e -aluate of v dx 2 se rationalizing substitution. 8

A: solution is given below

Q: Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos in polar coordinate…

A: Here we have to find the value of r and then plot the polar graph.

Q: Which of the following integrals gives the arc length of the polar curve r = cos 0 sin 0 for 0 ≤ 0…

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Q: y" − 3y' + 2y = 4e²t ; y(0) = −3, y '(0) = 5 —e2t4e2t + et 7 7 (1+t)4e²t - 7et 8e2t - 7et -e²t 4te²t…

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Q: The force on the triangular plate that is submerged in water as shown below waters surface 6m 4m is…

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Q: Illustrate the angle 5π Answer in 20mins

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Q: Find the volume of the parallelepiped determined by the vectors (0, 4, −5), (2, 0, 5), and (-1,3,0).…

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Q: evaluate * √2 2 dw √11+10w-w² O = -0.7973 O=-11.574 = -0.7297 One Hand on Pen, Other on Phone, One…

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Q: x² 8. (x) tan 3x+cot 3x 9.f(x) = 2 sin 4x cos 4x =

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Q: b- dy +2y=0; y=1 at t=0, y(0)=1 dt

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Q: ¹ (²³) 4- If f(r) = cot-1 + tan-¹ prove that f'(r) = r²+4

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

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Q: Q4) Find the maximum eigen value for the system 4 = x¹ (0) = (1 1) 4 with initial vector

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Q: The directional derivative of f(x,y,z) = In 1+yz from P to Q(-1,-1,2) is given by .... .(Correct to…

A: Given :f(x,y,z)=lnx21+yz-3xz2

Q: Sketch the graph of the function f(x): = 2x-3 x²-4

A: The function is  f(x)=2x-3x2-4

Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: If web₁x-b₂y-b3z, w= where b₁,b2, b3 are constants and b² + b² + b = 1. Show that 8² w 8² w 8² w əx²…

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Q: The force on the triangular plate that is submerged in water as shown below waters surface 6m 4m is…

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

A: Here, the given curves are: y=2x-x2 &amp; y=0 The area bounded by the curve is:

Q: Which ONE of the following is NOT the critical point of the function f(x,y)=xye OA (-1,-1). B. None…

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Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

A: Use volume of solid of revolution formula for finding the volume

Q: The series representation of f(x) = n(x²-1) is given by power OA ¹+¹, -1<x<1. n=] } + [ B. None of…

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Q: Put the given function into vertex form. Fill in the blanks to complete the function below.…

A: The vertex form of a quadratic equation is y = a(x-h)2 +k

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 region is bounded by y = x³, y = 2x + 4 and y=-1. Then Arearegion= = ["f(x) dx + ["g(x) [*g(x)…

A: The region is bounded by y=x3, y=2x+4 and y=-1. Then Arearegion=∫abfx dx+∫bcgx, where a&lt;b&lt;c.To…

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: d'y dx2 -sec³t -csc³t Find a. O b. O c. sec³t Od. csc³t Oe. in terms of t of x = sint, y = cost none…

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Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

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Q: Find the volume of the solid obtained by rotating the egion bounded by y=x+1₁ y=0, about y = -1. y =…

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Q: Suppose that x = 2 tan 8. What is sec e equal to in terms of x? √4+x² 2 √4+x² X Option 1 Option 2…

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