Evaluate the limit using L'Hospital's rule 1 lim 12xe 12x x →∞

Q: Given A = -1 0 22]₁ compute 3A

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Q: What is the average rate of change of the function f(t) = t² - 7t between t = -5 and t = -4? -16 -14…

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Q: Find where it increasing and decreasing x^5-2x^4+3x^2-5x+

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

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Q: Find the horizontal asymptote(s), if any, of the curve f(x) = (x-x+) -16 Select one: Ⓒ x = 4, x=-4 O…

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Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: Volume of the sphere , V=43πr3

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: If f(x, y) = 9x² - 6y³ - 7 cos(-6xy + 플) then Select one: O True O False fy(л,0) = -42

A: Given function is f(x,y)=9x2-6y3-7cos-6xy+π2. We have to find fy(π,0) that is partial derivative of…

Q: If u = (0, 2, 3) and v = (1, 3, -1), find the projection of u onto v. 이름다 a) Obl 이유ㅎ ○ c) (1, 1, -1)…

A: This question can be solved using the concept of vector projection of a vector on other vector.

Q: Minimizing Costs For its beef stew, Betty Moore Company uses aluminum containers that have the form…

A: Given  v = pi r^2 h = 45 h = 45/(pi r^2)   the metal used is just the surface area a = 2*pi r^2 + 2…

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

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Q: Use Leibniz's rule to find 히증 11 Textbook dx for y= 0 S 7x² 8t - dt. 8t+1 Ask my instructor

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Q: 01. |x2 - 1\dx = a. b. 2 C. 432 - 23 23 d. 틀-

A: This question can be solved using the concept of definite integrals and modulus function.

Q: 2 +81 1/s(3² +9) ²0 ds

A: The given integral is (s4+81)/[s(s2+9)].

Q: An equation of the form t²y" + aty' + ßy = 0, t > 0, where a and are real constants, is called an…

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Q: Find the following Wronskian: W(4, 3t, e-³¹, te-³1) O-972e-6t 0-972e6t 6 972e6t O 972e-6t 00 O-6

A: We can find the Wronskian .

Q: - 2. (x²y² + xy + 1)ydx + (x²y² − xy +1)x dy = 0

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Q: 3. Evaluate tan¹x² 1+xº dx

A: dtan-1(x)dx=11+x2

Q: 1/4 1 1/12 √√x (4x + 1) √x (4X - dx

A: See the details solution in below

Q: Find B in the partial fraction decomposition: 0-170 6 O 16 O 0 - 11 O - 5 6 none x²+2x+7 x3-10x2+21x…

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Q: 4. Graph the equation: f(x) = -3, 4, 1/² x + 1²/₁ x<-2 -2 ≤ x ≤ 1 1 < x≤ 4 -3 - 5+ 4+ 1 + 3+ 2+ 1…

A: f(x) = -3 , x &lt; - 2 x -3 -5 -7 f(x) -3 -3 -3 f(x) = 4 , -2 ≤ x ≤ 1 x -2 0 1 f(x) 4 4…

Q: Which of the following rational functions is equivalent to the partial fraction decomposition 2x 2x…

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Q: A spherical rubber balloon is inflated with air. The volume of the spherical balloon of radius r…

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Q: Exercise: 11 [ Solve the non-exact differential equations (Apply Rule IV)] 2. (xy³+y) dx + 2 (x²y²…

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

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Q: 6. If z = x + iy = (x, y), then the equation z²+z+ 1 = 0 is written as (x,y)(x, y) + (x, y) + (1,0)…

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Q: Find the centroid of the region bounded by the graphs of the equations using any method. y = √9-x²,…

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Q: II. Answer the following questions. Write the complete solution set on a clean sheet of paper. -0-…

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Q: 253-45-8 (5²-5) (5²+4) 253-15-8 s(5-1)(5²+4) Focusing on 5(5-1) (5²+4) A+B (3-1) S on denominator +…

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

Q: The domain of the function f(x, y) None of these This option D= {(x,y) = R² + +1} This option. D=…

A: We want to find the domain.

Q: 2x² sin x + 3y³ lim (x,y) →(0,0) 3x³ + 2y² if we approach along y-axis, we will get 0. Select one: O…

A: To determine whether the following statement is True or False.limx, y→0, 0 2x2 sin x+3y33x3+2y2if we…

Q: Find f tan 0 de. ] a. C. - In sin 0+ C - In cos 0+ C sec² 0 + C - In sec 0 + C

A: Here we have to solve the integral.

Q: 2) Find the indefinite integral by using the method of partial fractions: 3x+5 x²-9x+18 S- -dx

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Q: Evaluate 1-(In x) x In x -dx

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Q: 1 S dx 1/2x² √√x² +4

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Q: 5. If z = x + iy = (x, y) then the Im(iz) is A. Imz B.-Rez C. -Imz D. Rez E. none of the above

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

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Q: 1 2 x² +6x+18 -dx

A: A detailed solution is given below. We know that, ∫dx(x+a)2+a2 =  1a tan-1x+aa + c

Q: Let f: [1,1]→ R be a function given by f(x)=2x-x2. Then the inverse image (preimage) of [0,4] under…

A: The answer is option D

Q: Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a…

A: This question is based on vertical and horizontal asymptote.

Q: 2. Evaluate J dx (cos³x sin³x)

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Q: Problem 1 Let = (1,2,3), 7=(2, 2, -1), and =(4,0,-4). Find 27+ 4-w. Problem 2 Let = (1, 2) and =…

A: To express vector v as a linear combination of u and w.

Q: Solve: x²y + xy' -n²y = 0 General Solution: y = C₁ *letters only a.x2n b. x-n a.xn b. x-2n c. x2n…

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Q: is

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Q: 9 Evaluate f 99√x 30-x2 -x² 2 dx.

A: ∫4999x30-x322dx

Q: 1 Give the antiderivatives of X The antiderivatives of 1 2 are

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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: Present a second order differential equation. Identify the corresponding auxiliary equation.…

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Q: x - 4y = 26²

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