Test: Test 2 (11 problems) In the following problem, begin by drawing a diagram that shows the relations among the variables. If w=-3x +2y-32² and z=x²-, find ow aw ow b. C. dz y dy ?w a. dy z aw b. ().-0 dz aw C. dz y dz Quer

Q: a) Find the derivative in its simplest form for the following function 1–tanx y = tan-1 ¹

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Q: 4. A hockey team plays in an arena with a seating capacity of 15,000 spectators. With the ticket.…

A: Let's find set the ticket prices for maximum revenue.

Q: cscxdx 5+ cos²x sin²x

A: solution:-∫csc25+cos2xsin2xdx,    {…

Q: Find f'(a) for f'(a)= 10x13 Answers Attempt 4 of 4 f(x) = 3 + 13x - 5x².

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Q: Using any of the methods discussed for both numerical differentiation and numerical integration…

A: Given:           ∫252x2-3xdx

Q: The interval notation for the set (xlx ≤4 or x>-2} is. [-2,4] A O (-2,4] BO R .CO DO [-2,4) EO…

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Q: Solve the equation x+7 x-3 X-7 is : x+3 Ø .A O R-{-3,3} BO R .CO

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Q: 7.Find of z = 2x³-5xy² 8²z xy

A: topic- partial differentiation

Q: Find by implicit differentiation, given that x²y - 2y4 = -4. Your answer could involve both x and y.…

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2x³+2x²+2x+6 1. Lim x3+4x+3…

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Q: Determine all solutions of the given equation. Express your answer(s) using radian measure. (Select…

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Q: The sum of two positive numbers is 20. Find the numbers if the product of the square of one and the…

A: We have to solve above question and the find the two number

Q: Lim x-0 e³ +ex -x²-2 sin² x-x²

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Q: Find all points c satisfying the conclusion of the MVT for the function f(x) = 7e-⁹x + 4 and…

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Q: 5- prove that - for sin Ꮎ dᎾ cose Ꮎ dᎾ

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Q: Let R(t) = (t²,1 − t², t) and r(t) = cost. Determine the parametric equations of the line tangent to…

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Q: So 0 Evaluate the integral, if it exists. exc 1+e2x dx

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Q: An architect is asked to design a game room in the shape of an isosceles trapezoid where the non…

A: Let's find fourth side length for maximum area.

Q: Find the gradient of f(x,y,z) = (x² + y² +z²) Vf|(1,2,2) = Oi+Dj+Ok (Type integers or simplified…

A: ∇f(x,y,z) = ∂∂xi+∂∂yj+∂∂zkf(x,y,z)

Q: A. Determine whether each integral is improper. If it is improper, give your justification. 1² d 4.

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Q: The distance from a point P₁(x1, y₁) to the line ax + by + c = 0 is lax₁ + by₁ + cl √² + b² Use this…

A: SOLUTION-

Q: A population of 800,000 microbes increases at the continuous rate of 4% per day. a. Carefully sketch…

A: Given: population of 800,000 microbes increases at the continuous rate of 4% per day. Find: sketch…

Q: 2. The Minimum point of y= 320

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Q: For f (x)=xl-2, then f(-2) =0 صواب

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Q: a²z 7.Find of z = 2x³-5xy² xy

A: Given double differentiation. First we find the partial derivative of z w.r.t y. Then we find the…

Q: What is the volume of the solid generated by the area bounded by y=x² and x=y², and revolved about…

A: Given curves y=x^2 and x=y^2

Q: Let f'(x)=(x-1)(x-3). Then f is increasing on a) (-∞,1]U[3,0) b) (-0,2] c) [1,3] d) [2,00)

A: Let f'x=x-1x-3

Q: What is the value of C?

A: We have to find the value of C.

Q: II. Solve the following problems. Enclose final answer. 8.A kite at an altitude of 200 ft. moves…

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We have to find the volume.

Q: 9. Name the polar coordinates of the point graphed below. 플 S ㅍ 3π 10 -0

A: one radial line show one unit radius here point is at 4 number so point is (4,π/3)

Q: 5 √₁ (2x² - 2. 2 (2x² – 3x) dx

A: We can solve the definite integration as below.

Q: II. Solve the following problems. Enclose final answer. 9. A gutter with trapezoidal cross section…

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Q: Suppose f"(1)>0. Then, a) f is concave upward at x=1. b) f is concave downward at x=1. c) f(1) is a…

A: We have to choose correct option.

Q: Solve y' = 6xy - 2x, y(0) = 12 u(r) =

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Q: The general solution of y" - y = x²ex + 5

A: To find the general solution of y''-y=x2ex+5.

Q: The length of a rectangle is increasing at a rate of 5 meters per hour and the width is decreasing…

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Q: 12 Rewrite with out rational exponents, and simplify, if possible: (169) 2 4n4√√AO 4n 4.5 BO 8n4…

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Q: The parabola 8x² + 5y = 0, opens upward. downward. to the right. to the left.

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Q: 4. Find 3x 2t dx/e²t dt

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Q: LAW OF GROWTH AND DECAY A radioactive material decays at a rate proportional to the amount present.…

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Q: The LCM (y2-16, y2 +8y +16 (y-4) (y+4) G

A: Given: y2-16,y2+8y+16 Steps for finding LCM: Find all the prime factors of each given number.…

Q: MY NOTES ASK YOUR TEACHER The rate of change of the function f(x) = sin(x) + csc(x) is given by the…

A: Verify the identity

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: Solid S is bounded by the surfaces z=x2+y2 and z=4-x2-y2

Q: 2. If y=x³e²x find y(n) and hence y(3). (v)

A: I am attaching image so that you understand each and every step.

Q: Write an equivalent expression using exponential notation: a3

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Q: Find the cross product a × b. a = (9, 0, -4), b = (0, 8, 0) Verify that it is orthogonal to both a…

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Q: Find the integral dx √=x² + 6x I

A: We know that ∫dxa2-x2 = sin-1xa+C

Q: Jse differentials to approximate 47. (Express as a rational number.)

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Q: 3. Lim In(x+1)3 x →∞0 6x

A: We can evaluate the limit as below.