QUESTION 5 Find the 2nd solution by reduction of order. y" - 4y +4y=0; y₁ = e²x

Q: Consider the following. x = et, y=e-2t (a) Eliminate the parameter to find a Cartesian equation of…

A: Given  x=et  ,  y=e-2t   Then we can find out cartesian curve by eliminating parameter 't' .

Q: 2 x³ dx -6 √x²-9 Evaluate O44√3 24√/3 34√5 34√3

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Q: Solve the initial value problem: y(x) = 0. dy da + 3y = 7, y(0) = 0

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Q: -1 xp(x + 1)zz² J

A: The given integral,        ∫-11e2x1+xdx

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Q: 9. Determine if the Mean Value Theorem for Integrals applies to the function f(x)=√x on the interval…

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Q: 52. If lim f(x) = 6 and lim, g(x) = 3, find x-2 (a) lim [5 f(x) - 4g (x)] (b) (c) lim [4 - xf(x)]…

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Q: Devise the exponential growth function that fits the given data, then answer the accompanying…

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Q: Definite integral

A: Given :Definite integral

Q: Suppose S. f(x) dx = 36, [₁² f(x)dx = 12, ²9(1 1. (2f(x) + +12g(x) — 4h(x)) dr g(x)dx = 24, and h(x)…

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Q: Find the arc length of the graph of y == 6 2x on the interval 2 L2

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Q: 7x (x+3)³ a. Find lim F(x). X-3 Let F(x)= b. Find the vertical asymptote of the graph of F(x). c.…

A: F(x)= 7x/(x+3)3  a) find the limit of F(x) when x tends to -3 .  b) find the vertical asymptote of…

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 4xyz + 6yz²…

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Q: Transform the given differential equation into an equivalent system of first-order differential…

A: Using substitution and differentiation,

Q: Verify that the function satisfies the three hypotheses of Roll's Theorem on the given interval.…

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Q: (b) r4 x x²-9 dx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If f(x)=2-3x². O a. O b. O c. lim h→0 lim h→0 lim 30 From first principles select the correct step.…

A: Given :fx=2-3x2

Q: Find fx and f, and evaluate each at the given point. f(x, y) = exy², (In 6, 2) = (No Response) (No…

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Q: What is the y-coordinate of the y-intercept of the secant line of the square root function at x=1…

A: Here we have to find the y-intercept of the secant line

Q: (b) pre every x + 2 if x≤2 2 F(x) = ) + x² = (x +7 if x>2 - CX pie where I on 5) Sketch the function…

A: The Solution is given below

Q: 3

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Q: 1.) Sand hole conical pile altitude always 1 4 of increasing when the 14 pouring from a the conical…

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Q: Find all values of x and y such that fx(x, y) = 0 and f(x, y) = 0 simultaneously. f(x, y) = x² + 5xy…

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Q: find the standard equation of the sphere with center (4,3,3) and radius 7

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Q: What is the general solution to ya dy dx ○ y = ±₁/2. + C 4x In(4) o y = +. o y = o y = + 4x In(4) +…

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Q: A chemical reagent is introduced into a bacterial population, and t hours later the number of…

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Q: (a) State the Fundamental Theorem of Calculus Part I √x (b) If G(x) = cos(t¹) dt, compute Gʻ(z). (c)…

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

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Q: (d²4)(d - 2)y=0

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Q: · F(x) = 5* (S₁²¹6 (√₁+ u²) du) dt

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Q: (12) Find the derivative of the function Y = cos (a³ + x³)

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Q: 6. (8x³ − 6x² + 12x − 9)dx (x²-1)³ √x 8. [ V4 – x2 xdx 10 9. § (2x³ + 5)¹⁰ x² dx 7. S - dx

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Q: Find the first partial derivatives with respect to x, y, and z. 3xz x+y aw əx Əw ?у Əw əz || W = (No…

A: This question can be solved using the concept of partial derivatives.

Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

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Q: Apply Descartes' Rule of Signs. Determine the number of possible positive and negative real zeros…

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Q: Question 3 [ For the system of linear equations -3x + 5y = 4 ny + 12x = -16 a) [: Find the values of…

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Q: The region is bounded by the curves of y = x² and x = y². Find the integral in line y = -1. Use…

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Q: Use the half-angle identities to evaluate exactly. sin 112.5° sin 112.5° = (Simplify your answer.…

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Q: S ³+3 dz

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Q: find the equation of the tangent to the curve y = x+2x^(1/3) through point (8,12)

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Q: The region bounded by y=-|x-2|+1 and the x-axis is rotated about the y-axis. A. Sketch a graph of…

A: Concept: The washer method: The washer method is the name for the use of the slicing technique.The…

Q: af The partial derivative evaluated at P is 6. əx Find the directional derivative of f at P in the…

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Q: Evaluate fx and fy at the given point. 5xy f(x, y) = (1, 1) 6x² + 3y²' fx(1, 1) fy(1, 1) = (No…

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Q: Sketch the region enclosed by the curves and find its area. 1 √1-9x2¹ Y=2 NOTE: Enter the exact…

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Q: Find the indicated limit by using the limits lim (x,y) → (a, b) [f(x, y) - g(x, y)] lim (x, y) → (a,…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate…

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Q: 14. Σ(-1), Inn n! n=1

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Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: -π/3 sinx-cosx sinx+cosx Evaluate f dx

A: To evaluate the following integral.∫0π3 sin x-cos xsin x+cos x dx

Q: Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the…

A: Here, the given parametric equation is: x=1-t2, y=2t-t2, -1≤t≤2