Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.) dx, x2 + 36 x = 6 tan(8)

Q: Set up the integral to find the volume obtained by rotating the region contained in9 = y = 1, and ax...

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Q: Compute the global extrema of f(x,y) = x² + 2y² on the domain %3D indicated: a) D = {(x,y) E R?:0 < ...

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Q: The orthogonal trajectory for x^ 2 =ce^ x^ 2 +y^ 2 is

A: Orthogonal trajectory

Q: 4. Find the area of the triangle with the vertices A(2, –3,4), B(-1,-2,2), and C(3,1,-3) then find t...

A: We will find the area and the angle of the triangle.Where points A, B,C are given.Below find the sol...

Q: 3. lim c-11 f(x) = ? f(x) = -49 %3D 4. For example, if lim f(x) = 9 and limg(x) -10, then (a)lim (f(...

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Q: Using Laplace transform, find the solution of the initial value problem. 5. y" – 4y = 6e³t – 3e-t, y...

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Q: 6. Using differentiation formulas, write the derivative with respect to x of the following. Find the...

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Q: The functions f and g are defined as f(x) = 5x – 2 and g(x) = - 7x². f and a) Find the domain of f, ...

A: The given functions are f(x)=5x-2  &amp;  g(x)=-7x2

Q: 1 Using a table of values, estimate lim 7. z-3 I - 3 а. 1 b. -1 c. - 0 d. 0 x + 4 Using tables of va...

A: Topic:- calculus

Q: An open box having a square base and hold a volume of 32 cubic inches. What dimensions will require ...

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Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O n...

A: Given fx is continuous between a and b

Q: A 28-ft ladder leans against a building so that the angle between the ground and the ladder is 75°.

A: FOLLOW next step

Q: Find an exponential function of the form P(t) = Pon' that models the situation, and then find the eq...

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Q: -2

A: To find the given limits from the given graphs.

Q: Which represents the Midline? (B) (C) (D) (A)- O A O c D

A: Topic = Functions

Q: An environmental study in a community shows that the level of a certain pollutant in the air is L(P)...

A: Given:  An environmental study in a community shows that the level of a certain pollutant in the air...

Q: (2x-3y+6)dx-(4x-6y+2)dy=0 in Linear two variables with POI

A: Here, the given differential equation is: (2x-3y+6)dx-(4x-6y+2)dy=0 The equation can be written as: ...

Q: Rewrite the following expression in terms of exponentials and simplify the result. (cosh 3x + sinh 3...

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Q: Find an equation of the tangent line to the curve at the given point. y = 9e* + x, (0, 9) y =

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Q: Slope of a tangent line at t1 = 6.0 and y = at? dy v = lim At-0 dt

A: Given that: y=αt2

Q: Using the definition of the derivative, find f'(x). Then find f'(-4), f'(0), and f'(4) whenm f(x) = ...

A: We can find the derivative as below.

Q: The answer is: Find the exact value of a in the given interval that has the given circular value. Do...

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Q: a) Find the inverse of the function. b) Sketch the graph of f (x) and f-1(x) on the same Cartesian p...

A: We can solve all the three parts as below.

Q: Given the ellipse 9x² + 16y²-144 = 0 a) determine the length of arc in the first quadrant.  b) det...

A: Given the ellipse 9x² + 16y²-144 = 0 a) determine the length of arc in the first quadrant.  b) deter...

Q: Find the abscissa of the centroid of the region between the parabola y = 9-x^2 and the line y = 1-4x...

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Q: Two forces, with magnitudes 2 N and 3 N, act on an object at 10° to one another. Determine the resul...

A: Given that: Two forces are: 2 N and 3N acting at 10° to one another.

Q: A function is in a form of y = ax^3 + bx^2 + cx + d. It has relative maximum at (3, 3) and point of ...

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Q: Direction: Find the derivative of the function. y=- -z+ 2e Select one: O y' = 4x? – 1+ 2e" O y' = 4x...

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Q: Graph of f 11. The graph of the function f is shown in the figure above. Which of the following coul...

A: Given that: Graph of f(x)

Q: If vector A is any non-zero vector, a unit vector in the same direction of A would be?

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Q: Evaluate the integral. In 2 2 e sinh 0 d0 - In 10

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Q: f(x) = 1 and lim g(x) 15. If lim = 2, then evaluate each limit. x→0 x→0 X f(x) b. lim x→0 g(x) a. li...

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Q: Find the points function' that have horizontal tangents when f(x) = x°-6x 6 On the graph of the

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Q: 7 x2 dx + 4x + 20 13

A:

Q: dx

A: Let  x-2 = t  Differentiating both sides dx= dt  

Q: Sketch one possible graph of a function f(x) defined on R that satisfies all the listed conditions. ...

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Q: Evaluate the following indefinite integral. -x-2 (a) dx dx (b) cos 0 sin Od0

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Q: 5. Evaluate the following and give at least 5 non – zero terms: п-1 n(n + 1) x + (2n – 7)(2n + 9) dx...

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Q: A. B. ET D G. 2.

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Q: Miscellaneous Operation on Complex Numbers 1.-22+1 2.(2 + i) 3.cos h(i)

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Q: Given f(x,y) = x-y-3xy³. Evaluate fdx O 14y-27y3 +C 6 O -6y³ + 8y/3+ C O 6x2 – 45x + C 4 O 2x2 – 12x...

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Q: I. Find the distance between the two pairs of points 1. (3, 5) and (6, 8) 2. (2, 5) and -4, -2) 3. (...

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Q: Evaluate the integral. (Use C for the constant of integration.) 7 V 1- sin(x) dx

A: Evaluating the indefinite integral

Q: How much work is done raising a 6 kg mass to a height of 18 m above the ground? (Use decimal notatio...

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Q: 11. In a sine wave: a) At what angle, or angles, is the amplitude increasing at its fastest rate? b)...

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Q: В. Find all vertical and horizontal asymptotes. 2x2 +2x+1 15. f (x) = 5x3+3x-5

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Q: Below is a value of cosh x. Use the definitions for hyperbolic functions and the identity coshx- sin...

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Q: Find the center of mass of the solid E bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0 and z...

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Q: B. Find the general equation of the following conic with the given properties. 2. A hyperbola with f...

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Q: D. Given the following polar equations, find the eccentricity and identify the type of conic; write ...

A: We know that the polar form of a conic with directrix x=±p and the focus at origin has form: r=ep1±e...