b) 2 1 dx x ln x

Q: 1) Evaluate the integrals: (a) f sin³ (2x) cos (2x) dx (b) sin³ (2x) cos (2x) dx

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Q: Let f(x) = 2x - 13. Determine f-1¹(x).

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Q: Determine whether the lines L₁ and L₂ are parallel, skew or intersecting L₁: x = 4 + 2t, y = -5 +…

A: L1 : x=a1+b1t , y =c1+d1t , z=e1+f1tL2 : x=a2+b2s, y =c2+d2s , z=e2+f2sthen Lines L1 and L2 are…

Q: Given the functions f(x, y) = 4 cos(4x - 6y) and g(x, y) = -6 cos(4x - 6y). af The partial…

A: Here we have to use the concept of partial derivatives

Q: Which of the following may indicate that the graph of the function y = f(x) horizontal asymptote at…

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Q: Use trigonometric substitution to find or evaluate the integral. (Use C for the constant of…

A: To use trigonometric substitution to evaluate the integral. ∫x38+x2dx

Q: To evaluate the integral /VF² we use Select one: x² +9dx Substitution with x = 2 tan 0, where -T 7…

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Q: ate ſ- dx 4x²+1

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Q: The domain of the function f(x, y) = 3xy 2+√4x2+y2-16 is:

A: Given problem:- fx,y=3xy2+4x2+y2-16  To find:- Domain of f(x,y)

Q: If limx-5 f(x) = 4, limx-5 g(x) = 2, and limx-5 h(x) = 18, what is the value of lim x-5 4f(x) + g(x)…

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Q: A rotating light is located 20 feet from a wall. The light completes one rotation every 3 seconds.…

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Q: 4. If z = x + iy = (x, y) then the Re(iz) A. Imz B.-Rez C. -Imz D. Rez E. none of the above

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Q: Which of the following is a valid expression for cos ¹ x? 04-sin-¹ a 01/2+ + sec¹ a 1 sec-1 01-…

A: The given expression is cos-1(x)We have to find the valid expression for cos-1(x)

Q: Work problem 2 (1 Let w(x, y) = 5x - 5y - x² + 5y³, x = cos(t) and y = -sin(3s). Use chain rule to…

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Q: with the initial condition y(1) = 4. -0 Y

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Q: If 2 cos 2t = 1/5 then sin² t = Select one: O True O False 13 30

A: We can find the answer as below.

Q: 4 Use the substitution z +9=u² to evaluate √√+9

A: Note: Since, the student has asked to solve only question no. 4, so we are solving accordingly…

Q: Determine any planes that are parallel or identical. (Select all that apply.) OP₁: -60x + 90y + 120z…

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Q: f(x, y) = Find fx, fxy, and fxyx. 7 8x+5 + 8x³ e-8y

A: The given function is;  f(x,y)=7/(8x+5) +8x3/e-8y.

Q: Find the indefinite integral by usi Integration by parts formula: 5

A: ∫ x5lnxdx

Q: Evaluate the following integral: sin²(a) da

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Q: 1. Find the domain of the vector function r(t) =

A: 1. Given Vector Function,rt = lnt+2, t1-t2, 2tt2 -4

Q: (5x¹2xy)dx + (6y+kx²)dy = 0

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Q: π sin" g 2. So cos² g dg

A: The given integral is;  Sin5g/Cos2g, limit from 0 to pi.

Q: z = e Select one: True False In (2-y), dz and x = s² - 6t, y = t - s, then the value of when t = 4…

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Q: Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of 8,…

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Q: 8. Use the graph of the function f to find the following: 13 (-5,0) 4 -3 -2 -1 (-3,-2) 3 2 H (-1,-2)…

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Q: f (x-2)(x+1)' 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 the area bounded by y = 4x -x^2 and x = 0, and y = 4 using two methods (vertical and horizontal…

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Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A: Concept: Using Left Riemann Sums and Non-Uniform Partitions, a Process for Approximating Definable…

Q: Evaluate f √x² - 16 8 -dx

A: use the substitution method for solving the integral.

Q: 22. Use the Rational Zero Theorem to help you solve the polynomial equation 2x17x³ +46x²-43x + 12 =…

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Q: Part c: ( 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1, -1). 2.…

A: We have to find the gradient and directional derivative.

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: Fill in the blanks Enter intercepts as ordered pairs, aka points. Then Graph the parabola given in…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Compute the following: fcos (x) sin(2x) dx

A: Given: ∫cos2(x)sin(2x)dx

Q: 8x³ - y³ 3 lim (z,y) (1,2) 2x - y Select one: O equals 12. O equals 0. O None of them O equals 4. O…

A: Lim(x, y) -(1,2)(8x3-y3)/(2x-y).

Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: Use implicit differentiation to find dy given y³2 – log(x²y¹) = cos¯¹(1). dx

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Q: Suppose f'(x) = x² - 1. Then the graph of f is concave upward on 0 (-∞0,0) O (-1,1) (0,00) O (-∞,…

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Q: (x, y) 5) 4x2+2y2 Find the domain of f. Show that the limit does not exist. lim f(x,y) (x,y) → (0,0)

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Q: If then fxx = Select one: True False 2(y² + y) (y - x)³ f(x, y) = x + y² y-x

A: According to question,Given Function,fx, x = x + y2 y-x

Q: Choose the correct answer for the following limit: x²-812 lim (x,y) (0,0) x +9y Select one: O A.…

A: We have to calculate the limit.

Q: Find the indefinite integral using any method. (Use C for the constant of integration.) [(sin(0) +…

A: We have to find integration in this question.

Q: swer of the following lim 2x²+6y² lim (x,y)→(0,0) x²+y²

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Q: 1. Let C be the curve described by the equation x³ + 3x²y-xy² = 3. dy dz (b) C contains the point…

A: Equation of tabgent to a curve y=f(x) at a point (a,b) is given by y-b=y'(a)(x-a)see below the…

Q: Write The Green's Theorem in the plane relating double integrals and line integrals. (Please, don't…

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

Q: Let z = √√√7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2. ds

A: