Evaluate the definite integral. e141 i + ej +t k )dt O e14 – 1 1 Li+ (e- - 1) j+, k 14 (e4 – 1) i- (e- - 1) j+ k O el4 1 i - (e-1 – 1) j + k i-etj+ (e-1 – 1) + -- 14 O e14 k 14 O el4 – 1 14 2

Q: Find the are bounded by the curve y=x²-4, the lines y=0 and x=4.

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Q: FinD THE arza BOUNDED By THE CURVES : y° +y +Z %3D

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Q: 5. SET-UP the double integral that solves for the volume of the solid: 3 3x+ 2y+ 4z = 12

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Q: f(x)=x-4/x^2+2x+17 What monomial expression best estimates the behavior of x-4 as x→± ∞ ?…

A: Given problem:- f(x)=(x-4) /(x2 +2x+17)    What monomial expression best estimates the behavior of…

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A: We have to find the point at which the line intersects the given plane.

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A: Ellipse

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A: Given query is to find the demand at given point.

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Q: Q4 Find the eigenvalues and eigenvectors of the matrix: 21 1 -1 2 -2 1-1

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Q: 4. Find the exact value of the expression. (a) 10log 36 (b) In e3

A: Explanation of the answer is as follows

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Q: mlar

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Q: Find the area of the blue region. It is the area under the curve. 8 y = 3 x + 1 4 y =7– x 2 4 6 8.

A: This question can be solved using the concept of area under curve.

Q: The demand curve for a certain product is given by p(q) = 541 - q. The supply curve is given by p(q)…

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Q: In Exercises 1-3, find the general solution of the differential equation specifie lip 2. dt 1+t

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Q: Use f(x) = 4x - 5 and g(x) = 3 - x to evaluate the expression. (a) f(g(0))= (b) g(f(0))=

A: Given query is to find the value of indicated function.

Q: Draw the Root Locus curve for the equation s (s + 2) (s + 3) + K (s +1) = 0.

A: We have to draw the root locus curve.

Q: 73 dx

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Q: Compute ||A|| ||A|l, and ||A|l 2 8 A = 35 %3D

A: Given

Q: Find thee inverse function. of fcas_ 2x+3 らメープ

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Q: Evaluate the indefinite integral. x2 dx 0.2x3 + 2.7 + 2.7

A: topic - indefinite integral

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A: Let,  ϕ=-8cosπx+3x2y+exz+5yz-15∇ϕ=i∂ϕ∂x+j∂ϕ∂y+k∂ϕ∂z…

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Q: 10 9. Consider the function f(x) %3D Let F(r) be the antiderivative of f(z) with F(1) - 0. Then F(x)

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Q: Use Newton's method to approximate a root of the equation +x + 4 =0 as follows. Let 1 = - 1 be the…

A: The given equation,    x3+x+4=0

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Q: In the video game Animal Crossing: New Horizons, there are 21 squirrel characters who can live on…

A: Given  There are 21 squirrel characters who can live on your island. We are allowed to have 10…

Q: Find the derivative of f(x) = log, (7x). (Use symbolic notation and fractions where needed.) df dx…

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Q: Given the differential equation y'' – 5y' + 3y = – 4 sin(5t), y(0) = – 2, y'(0) = 1 | Apply the…

A: Given,  y"-5y'+3y=-4 sin(5t)

Q: Consider the region bounded by x = 3y and x = y^2. A solid is formed by rotating the region about…

A: We have to set up the integral to find the volume.

Q: ¤(x+4)~²dx

A: Here we have to find the given indefinite integrals.

Q: The best substitution to use for the integral sin z V1+ cos z dx

A: when we substitute, u = 1 + cosx then the value of du = - sinx dx

Q: Find the expression of the general term of the sequence given by 3 5 7 9 11 1, 2'6' 24' 120 ' 720 2n…

A: The given sequence,      1,32,56,724,9120,11720

Q: 5. Use the Laws of Logarithms to expand the expression. x + 2 3 (a) log (b) In y (c) log. x(x² + 4)

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Q: Given the following matrices. -6 -2 -4 1 0 10 [C] = and [D] = 6 -7 1 -6 -5 -7 7 -9 -1 Find [C] [D]"…

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: (c) in the tank to a height of 1 m above its top. Give a definite integral that computes the total…

A: answer is in next step

Q: 2. (6x -2) dy d2

A: In the given question we will use the formula for that double integration ∫x=pq∫y=rtfx,ydydx Where…

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Q: Find the particular solution of the following ODE given that y(0)=7 and y'(0)=0: d’y dy dx -+3-10y=0…

A: To find the particular solution of ode

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Q: (d) 10*+3 = 62r

A: Given,  10x+3=62x

Q: Given: (1+5x, X<-1 f(x) ={ x2 -3, -1 <x<3 7x-6, x23 Determine (if possible) f(-1) a. None of these…

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Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

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

Q: 3. Using the graphs of the functions f and g below, determine the following. If infinite, specify ∞…

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A: Directional derivative

Q: Find an equation of the plane. The plane through the point (7, 0, 5) and perpendicular to the line x…

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Q: The state of Alaska allows for the following sequence on license plates, 2 letters followed by 3…

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