x < -3; x + 3, V9 – x², -3 < x < 3; 6 – x, h(x) = x > 3.

Q: Direction: Solve the following equations using separation of variables. 2. y' = x(1+ y²)

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Q: where does this concave up and down?

A: A graph is concave up if f''x&gt;0 and concave down if f''x&lt;0. When f''x&gt;0, it means…

Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

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Q: Ina swimming pool measuring 90 m by 40 m, 150 men take a dip. If the average displacement of water…

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Q: 2pq If sin A = ,where A is an acute p2+q² • angle of a right triangle, what is sec A? p² + q? p² +…

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Q: Determine the direction cosines and direction angles for Á =

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Direction: Solve the following equations using separation of variables. 4. sin(x)dx + ydy = 0, y(0)…

A: Given

Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). X→ー0 2x4 +3x +2 f(x) =…

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Q: 3. y = ln³(x + sin x) 4. y = tan¬1(3x) cos 1 4x G ED DI 5. y =

A: All the questions are a solved below.

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (6, 2, 32)…

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Q: For the function glven below, use algebra to evaluate the limits lim f( メー→+ lim f(x), and limf(x)…

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Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations hat are…

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Q: The length and breadth of the floor of a room are 30 feet and 20 feet, respectively. Square tiles of…

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Q: 2. Find the equation of tangent line and normal line to 3x y3 + 2y =1 at (0.2) (15 points)

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Q: For an integral of the form f sin™(x)cos"(x)dx, saving one sine factor and converting the rest to…

A: Given data÷

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (2, –3)…

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Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

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Q: Find the inverse of the matrix 3 0 2 -1 1 A= -2 -3 1 1 글 0 를 글 0 를 0 글 1 1 0 글 를 0 글 1/2 1. 112 112…

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Q: Consider the function y = 3(square root of x) + 8. What is the value of C in the interval [4, 9]…

A: First we will find fave

Q: J arctan x dx A C In(x2) + C In(x² + 1) + C x arctanx x arctan X - | 1. x arctan x +- In(x2) + C x…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: To find out the directional derivative.

Q: 2x

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Q: how about the equation of the normal line?

A: Apologies for the inconvenience. Here is the solution for the normal line:   From the original…

Q: The length of a rectangle is two-fifths of the radius of a circle. The radius of the circle is equal…

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Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: If the surface area of a cube is increased by 96%, by how much has the edge increased? 96% 92% O 40%…

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Q: 2. Find an equation of the sphere satisfying the given conditions. a. It is concentric with the…

A: In this question, we want to find an equation of a sphere which is concentric with the given sphere.

Q: A rancher wants to fence in a rectangular area of 18000 square feet in a field and then divide the…

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Q: Derivatives of trigonometric functions Find the derivative. 1. y = 3sin x +3 cos x - tan x

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Q: | cos'x cot x dx 3.

A: To integrate the given.

Q: s the volume of the frustum of a cone whose upper base is 16 cm in er, lower base 10 cmin diameter,…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: Determine the maximum volume of a cylinder that can be inscribed in a sphere with radius of 10cm.…

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Q: total

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Q: 21.3 xdx V16 - 9х4 0.

A: We to integrate the given integration.

Q: Consider the following. u = 5i - j - k, v = -i + 5j + 2k (a) Find the projection of u onto v. (b)…

A: The expression for the vector projection of u onto v is: projvu=u·vv2v And The expression for the…

Q: Let S be the solid obtained by rotating the region shown in the figure about the y-axis. a = 4 b = 2…

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Q: y^2= (x^2 + 2x)/ x-1 find the x and y intercept, symmetry, region/scope, asymptotes, critical…

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Q: 1. write the slope-intercept forms of the equations of the lines through the given point (a) paralel…

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Q: A function f(x) has a critical number x=c. Which of the following statements is always true about…

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Q: If f(x) = e*sinh x, what is f'(x)? e*(cosh x- sinh x) O Option 1 Option 2 e*(sinh x - cosh x) 2e2x…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y²,…

A: Given: f(x,y)=x2-2xy+y2, (5,7,4).

Q: Direction: Find the differential equation of the family of curves described. 3. Find the family of…

A: We are asked to find the family of curves of straight lines with slope and `y` -intercept equal.

Q: 1. Determine whether the following integrals converge. (a) 1 dx x3

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Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: Find the dot product of v and u and determine if the vectors are orthogonal. a. v = , u = The…

A: There is more than 1 question, as per the Q&amp;A guidelines we are answering the 1st question. If…

Q: Find the dot product of Á = and B =. Find the scalar product of P = 10î – 4ĵ + 7k and Q = -2î – ĵ+…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: 5. Given the equation: (x + 2y – 4)dx + (2x – 4y)dy Solve the differential equation. Choose your…

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Q: The shaded region shown below is bounded by the functions f(x) = -4x? + 10 and g(x) = x + 6 and the…

A: area