In(x) x² -dx

Q: Find the first derivative of f(x) ƒ'(x)= = 8x + 10 19 x

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Q: 5-6 Find the area of the shaded region. 5. y = x³ - 3x (-2, 2) YA 0 (2, 2) y = x X

A: Application of integration

Q: Compute the directional derivative of the following function at the given point P in the direction…

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Q: Given the equation for a “tilted” ellipse: x^2-xy+y^2=3 . Find the points (x, y) on this ellipse…

A: Here we have to find the largest and smallest values of x.

Q: Find the two places on the curve y = x¹/³ - 8x²/3 x4/3 Y where the tangent is horizontal. (a) The…

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Q: Suppose that ƒ(x, y) = 4x + 4y on the domain D = {(x, y) | 1 ≤ x ≤ 2,x² ≤ y ≤ 4}. D a Then the…

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Q: Find all critical points and then use the first-derivative test to determine local maxima and…

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Q: Explain the meaning of direction angles and their relation to direction vectors. What are the…

A: Answer: As per the guidelines, we can solve only first 3 subparts only, so post remaining parts…

Q: The linear approximation at x = 0 to sin(8x) is A + Bx where A is:

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Q: Find the acute angle (in degrees) between the planes x + 3y - 5z = - 6 and 2x + y 4z = 9. Question…

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Q: 7. Set up the integral for the total fluid pressure of on the plate submerged in water in the…

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Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1,100- dv V…

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Q: Evaluate the triple integral over the indicated bounded region E. JIS (x + 2yz) dV, where E = {(x,…

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Q: Let F(x, y, z) = (x², 2xy + e³², 3ye³z). Find div F(1,2,0) and curl F(0, 1, 1).

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Q: QUESTION 6 Use any method to evaluate the integral. 6 cm³ x dx tan x S O-2 csc4 x+C csc4 x cotx + C…

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

Q: Find the antiderivtive: 3x5+2x²+3 x8 - dx = + C

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Q: ax Find the value of a so that the function f(x) = xex has a critical point at x = = 3.

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Q: Find 3 4 [² 6² ² 2 2 x + y dydx.

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Q: J sin’rVcos ad

A: Here is the solution:

Q: Find the values of m and b that make f differentiable everywhere. Sx² m = b = f(x) = mx + b if x ≤ 5…

A: Here we have to find the value of m and b.

Q: sin 0 cos² 0-cos 0-2 2. S. de 3. fx² tan-1 (1) dx 4. f(cot ¹ x + tan-¹ x) dx

A: The given integral is;  3) x2tan-1(x/2) 4) cot-1x+tan-1x.

Q: Determined from First Principles and use your result to find the slope of the tangent dx at x = 2…

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Q: By considering different paths of approach, show that the function below has no limit as…

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Q: 7) Use the method of Undetermined Coefficients to solve y) +2y"+y = 3 sint - 5 cost. You can use…

A: Please see the below picture for detailed solution.

Q: Maximizing Profits An apartment complex has 100 two-bedroom units. The monthly profit (in dollars)…

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Q: Find dy/dx in terms of x and y if arcsin(x¹y) = xy¹. dy = dx

A: Solving the following problem

Q: Find a function ƒ(x) such that ƒ'(x) = −8x² + 1 and ƒ(0) = 1 ƒ(x) = |

A: f'(x)=-8x2+1f(0)=1∫xndx=xn+1n+1+c

Q: Use Newton's method to approximate the value of 45 as follows: Let 13 be the initial approximation.…

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Q: The Sumeru Akademiya wants to manufacture Canned Knowledge in literal cylindrical cans that could…

A: a. The cost of production C can be modeled as: C(r, h) = 2πr^2(0.02) + 2πrh(0.01) Where the first…

Q: A manager estimates the daily output of their robot model OYW931 at one of their factories to be…

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Q: Find the surface area of the part of the plane z = 3+ 7x + 6y that lies above the rectangle [1, 6] ×…

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Q: Solve the initial value problem. Ꮎ +y=3 sin 0, 0>0, y dy de E|N = 1

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Q: Maximizing the Volume of a Box A box with an open top is to be constructed from a square piece of…

A: Four square pieces at the corners of a square cardboard of size 12 × 12 Inches  And it was made into…

Q: Explain how you would prove if four given points are coplanar. Use the method you described to…

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Q: Find the distance from the point (-1,1,5) to the line ä(t) = (- Question Help: Video

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Q: since you cant find an inverse, how do you prove the function is one to one so that you can still…

A: Given: y = 2x + x3Aim: To prove that the y = fx is a one-to-one function. Basic information:A…

Q: The Sumeru Akademiya wants to manufacture Canned Knowledge in literal cylindrical cans that could…

A: Let h be the height of the cylindrical can and r be its radius.   Volume of cylindrical can can be…

Q: 5. Set up the integrals for the volumes of solids of revolution by revolving the triangu templates…

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Q: Give the derivative formula for the function. g(x) = 6x2/3 − x−1/3

A: To find the derivative

Q: Determine if f is continuous at all possible points of discontinuity. Classify each discontinuity as…

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Q: how do I find the inverse of f(x) = 2(√x) + x^3

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Q: The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV =…

A: The pressure, volume, and temperature of a mole of an ideal gas are related by the  equation…

Q: Add as indicated. Express your answer as a single polynomial in standard form. (x² + 4x +9) + (8x-7)…

A: The given expression is: x2+4x+9+8x-7  Express as a single polynomial in standard form.

Q: Assume C is a circle centered at the origin, oriented counterclockwise, that encloses disk R in the…

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Q: At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship…

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Q: Find: U(x1, x2) = 2X1X2 O X1X2 2x1 2 2x2

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Q: If the vector field F = (f.g) is source-free (zero divergence), then a stream function y exists such…

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Q: Give the derivative formula for the function. g'(x): = g(x) = 8 X + e¹2

A: The given function gx=8x+e12. We have to find the derivative function g'x.

Q: AB2: Let G(x) = ef(x). Find G'(6). AB3: Evaluate xf'(4-x²) dx S²x₁

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Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…

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