N g'(x) = Find the derivative of the function g(x) = (3x²5x + 1)e²

Q: A rectangle is inscribed inside the curve y = √9 -x in the first quadrant so that the base is on the…

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Q: Find the area bounded by the curve y=x^2 and the x-axis and the lines x=1 and x=3.

A: Given: y=x2, x=1, x=3, and x-axis or y=0. So, from the given curves the bounded region is as shown…

Q: 6) Identify the vertical and horizontal asymptotes of (x)= x-4 - 2x+17 b. vertical-x- 4, horizontal:…

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Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-tIn(t) y(t)

A: Given the differential equation is y''+2y'+y = e-t lnt

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: Given: f(x)=1+3x-5x3

Q: Find all values of x and y such that Px(x,y) = 0 and P Py(x,y)=0 simultaneously. P(x,y) = 5x² -…

A: Topic = Algebra

Q: 1. Find and classify all critical points of the function f(x, y) = x² + y²-3x - 4y.

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Q: 2-8-7-5-9-4-8 6-of-it-ct-st- t-t-et-Lt-st-et-at- Find an equation for the graph above. laruto 34 3 2…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find all solutions of the equation 4 cos(3θ + π/4)+2=0 in the interval [0,2π].

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

Q: Given the diagram of the bounded area, The limits of integration Choose Area in square units is X is…

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Q: What intervals must be considered for finding solutions to the inequality x > 5-º? C. 03 d. x 3 a.…

A: Follow the procedure given below.

Q: Which of the following is a power series representation of f(x) f(x) = Σ(-1)". n=0 8 x2n f(x) = Σ 16…

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A: We will solve.

Q: We have verified that x² and x are linearly independent solutions of the following second-order,…

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Q: Which of the following planes is normal to the line given as: x = 2t + 3, y = 5t - 7, z = t - 4 O a.…

A: This question is based on dot product.

Q: (4x²y² - x² + 4xy² - x) dx + (2xy + x + 2y + 1)dy = 0

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Q: Find the indefinite integral by making a change of variables. 1 √ 4 + ²√2x² dx

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Find y" in Exercises 71-78 1 X 71. y = 1 + 3

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Q: y'(x) = 49e²7 -46₂2642 де +2.4e4x + 9.6ne 422 -4 HOW DID HE GET THE VALUE INSIDE THE CIRCLE, CAN YOU…

A: We need to find y'(x).

Q: Determine whether the given set of functions is linearly independent on the interval (-∞o, co).…

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Q: Find the centroid of the region bounded by the graphs of the functions y = 3x², y = x² + 4 The…

A: Centroid Of the Region :           x¯ = 1A∫x=ax=b xf(x)-g(x) dx  and   y¯ = 1A∫x=ax=b 12fx2-gx2 dx…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: Find the determinant. x² -Ed 2x 5x4 W(x5, x²) = = (x²)(5x4) - (2x)(x5) The Wronskian ---Select---…

A: We need to fill in the blanks.

Q: 1) State the vertical asymptotes of f(x)= a. x=6₂x=-2 b. x=6, x=2 1 x² - 4x-12 c. d. x=-6, x=-2…

A: Given:         fx=1x2-4x-12 Vertical Asymptote:     For rational functions,the vertical asymptotes…

Q: Consider the following. u = (-10, 0, 8) v = (5, -9, 0) Find u x v. Determine if u x v is orthogonal…

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Q: WHAT IS O H|5 Se-5x dx 1 e -5x + C -e e-5x + C -¹e-5x + C 5 e-5x + C

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Q: | (8z + 4z³ - 6z²) dz? O 16z²+z4-2z³ + C O4z²+z4-22³ + C 16z²+z4+ 2z³ + C O 42² +224 + 2z³ + C

A: Solution: ∫8z+4z3-6z2dzApply the sum rule=∫8zdz +∫4z3dz -∫6z2dz

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing.…

A: increasing and decreasing intervals of fucntion  fx=3x4 − 4x3 − 12x2 + 5

Q: 8) How many solutions does the equation a. 0 b. 1 X+5 x-3 IX 1 || 4 x²-3x C. 2 d. 3 have?

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Q: t Let f(x) = 4x4 + 6. (a) Use the limit process to find the slope of the line tangent to the graph…

A: NOTE: Refresh your page if you can't see any equations. . the given value is x=4 the point on…

Q: 15) I What is the average rate of change of f(x) = from x = -2 tox = 4? x-s X+3 b 24 7 M C. d. 25 21…

A: We know that the expression for the average rate of change between the interval x2≤x≤x1 is: Average…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: 6. Evaluate the following real integrals by residue theorem 3 T 211 I- -S do coso + 2 sing +3 ans o…

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Q: Find the gradient of the function at the given point. Function g(x, y) = ye-x Vg(0, 9) = Point (0,9)…

A: Given function: g(x,y)=ye-x

Q: 21 (a) ²x¹ d(x³). Note a(x) = x³. 3 (b) (²x² d(ex). Note a(x) = ex 2

A: Given :∫1213x4dx3∫24x2dex

Q: Find the composite functions (f. g) and (g°f). What is the domain of each composite function? domain…

A: Given: fx=x6gx=x6

Q: 9. Consider the function y = 22 with derivatives 2(6-2) dr² Find any horizontal asymptotes of the…

A: Concave Up , if the second derivative is positive . Concave down , if the second derivative is…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive.…

A: We will use standard method to solve this.

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: Solve the following ODES by Undetermined Coef D Ş 17 4X y - 16 y = 19.2 e + 60e, y(a) =ý (os. 4X -4X…

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Q: Sketch the region R and evaluate the iterated integral -1.0 O [²L²¹²- -0.5 (12x+8y) dy dx y 3 £₁ […

A: We can evaluate the given integral by using the integral formulas.

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by L(x,y)=…

A: Given :Lx,y=32x2+y2-3x-6y-2xy+101

Q: Find the general solution of the given second-order differential equation. 9y"+y' = 0 y(x) =

A: General solution of real roots is used.

Q: Find the area between the curves. x = -5, x=2, y = 2x² +5, y = 0 The area between the curves is…

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Q: 4. In a chemistry class, the students in a lab derived a function to model the results of their…

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Q: (2xy - x + 2y - 1) dx + (8x² y² -2x + 4xy² − x) dy = 0 -

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Q: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) =

A: The DE is given as , y''+2y'+y=e-tlnt find the solution by variation of parameters.

Q: Solve the initial value problem by Laplace y" +4y=20 e y(0)=3, y'(0) - 12

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Q: Module A car dealership increased the price of a certain car by 4%. The original price was $44,400.…

A: As per given question  We have to determine new price of car