The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e² dt - ₁2(e²t - 1)t dt √(1-1²)e² dt (2-1)-(1-6)* 2t [²√(20)² +42² # -

Q: Differentiate the function (5y 1)4 /y2 1 G(y) In =

A: Given information:

Q: Evaluate cex-y) dx + C (x+3Y) dy C:xaxis from (0,0) to (0,-3) and 0-3) to (5,-3).

A: To Evaluate: ∫C2x-ydx+x+3ydyC: x-axis from 0,0 to 0,-3 and 0,-3 to 5,-3.

Q: (1 – x)y" + 2xy' = 0 , y1

A:

Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: Verify that the time needed for y(t) = y0ekt to double from y0 to 2y0 is thesame as the time needed…

A:

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: Determine the NATURAL cubic spline S(x) that interpolates the data f (1) = 1, f (2) = 1, and f (3) =…

A: The given data  is x0=1 , x1=2 , x2=3 and fx0=1 , fx1=1 , fx2=0. The spline polynomial will consist…

Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Find the tangent line at t=1/2 for the graph given by x=4+4ln(2t) and y=t2+10 for all Real numbers…

A: The given curves are x = 4+4ln(2t) and y = t^2+10.In order to find the tangent line, first find the…

Q: For HEE EN x'(t) 10 0 ( 1) : х (0) у' (1) =| 0 1 -1 у (г) у (0) 1 z'(t) 0 1 1 z (t) z (0.) 1 Write y…

A:

Q: Find the derivative of the dot product (u(t) • v(t)) if u(t) and v(t) equal the following (see image…

A: Given vectors are we are to find the derivative of u(t).v(t)

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

A:

Q: . Sketch the level curves of the function f(x, y) = x² + 2x + y² – 6y corresponding to the z-values…

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Q: Exl. suppose the pdf of r.v. X is [x/8, 0<x<4 fx(x)= {*/8, 0<r<4 . Find the pdf of Y =-2X +8. 0,…

A: Y= - 2X + 8, we have dydx= - 2⇔ dx =-dy2and 0&lt;x&lt;4 ⇔ -8&lt;-2x&lt;0 ⇔0&lt;-2x+8&lt;8⇔…

Q: b) Evaluate the value of I = S(eºy − 3x) dx + (6xey + y)dy, where C' is the parabola y = C (0, 0) to…

A: The integrand is given here as         (e6y - 3x)dx + (6xe6y + y)dy        = (e6ydx + 6xe6ydy) -…

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

A:

Q: Determine the NATURAL cubic spline S(x) that interpolates the data f(1) = 1, ƒ(2) = 1, and f(3) = 0.

A:

Q: (t4)d4y/dt4 +(7t3)d3y/dt3 +(3t2)d2y/dt2 - (6t)dy/dt +6y = 0 takes the form of y =tr for constants…

A: