1. Evaluate these integrals either by substitution or by integration by parts: cln 2 et a sin(2r) dr | x In x dx dx 3+ 2e* dx

Q: Determine whether the geometric series is convergent or divergent. n=1 (-6)n - 1 O convergent diverg...

A: Let's find. 

Q: Find the volume of the solid enclosed by the paraboloids: z = 2x2 + y2 and z = = 27 – x² – 2y2. 5.

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Q: g(b). Use the Substitution Formula, -g'(x) dx = f(u) du where g(x) = u, to evaluate the following in...

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Q: Evaluate the integral. X-7 dx X-7 dx = 8 %3D

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Q: Use the alternative form of the dot product to find u · v. |lu|| = 50, ||v|| = 20, and the angle bet...

A: Given: u=50, v=20 and angle between u and v is 5π6 We know that u·v = uvcosθ, where θ is the angle b...

Q: If r = 26 cm, what is the area of this sector? Express your answer to the nearest tenth of a centime...

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Q: Give two other polar coordinate representations of the point, one with r 0. (r, 0) = ( 3, – 2.14 X ...

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Q: Given the graph of y = f(x), sketch the graphs of f' and f" on the same set of axis. 1.

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Q: cos 4x 2 dx sin4x 5.

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Q: dx cot 3x sin 3x -1/3 sec 3x + C

A: ∫dxcot(3x).sin(3x)=∫dxcos(3x)sin(3x).sin(3x)

Q: Sketch the region bounded by the given curves and find its centroid

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Q: The intensity of an earthquake can be measured on the Richter scale according to the following logar...

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Q: SOLVE THE FOLLOWING 14. = In (x² + 1) 15. = In (Inu)

A: As per bartleby guidelines we only give first question answers. 

Q: b b-a b-a Use the equation f(x)dx= lim 2 fa+k- to evaluate the following definite integral. n→0 k = ...

A: Given query is to find value of the integral.

Q: Explain why the function is differentiable at the given point. f(x, y) = x³y?, (-2, 2) The partial d...

A: L(x,y) = fxx0,y0x-x0+fyx0,y0y-y0+f(x0,y0)

Q: Evaluate the integral. 3* dx 3* +4 Solution:

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Q: Let a, b, and c be three-dimensional vectors. Identify whether the expression (a x b)- (c × d) will ...

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Q: 3xey + yex = 4   Find dy/dx by implicit differentiation

A: Please see the answer below.

Q: The winner of a "million dollar" lottery is to receive $50,000 plus $50,000 at the end of each year ...

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Q: g(b) Use the substitution formula, f(g(x)) g'(x) dx = | f(u) du where g(x) = u, to evaluate the foll...

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Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into ...

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Q: Consider the following function and express the relationship between a small change in x and the cor...

A: Given f(x)=cot 8x

Q: Determine the continuity of the following functions. Determine continuity, if applicable. the kind 9...

A: To check the continuity of the given functions.

Q: 2. S cos-1 x dx

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with ...

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Q: Let f(x, y) = xr sin(xy). Find (a) xy cos(xy) (b) y cos(xy) (c) x² cos(xy) (d) -x sin(xy) (e) Some o...

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Q: write the equation in spherical coordinates a) 3x2 − 4x + 3y2 + 3z2 = 0

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Q: Find an equation of the plane that is normal to the surface Iz + yz? = 2+ yz at the point (2,-1, 1).

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Q: 1 リ=ス,メ=0; Xe2, y=or abt. A the x- Axls

A: Given

Q: Find Partial Derivatives for z = sin(x)cos(xy)

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Q: Use areas to evaluate the integral f(x) = 3x + 9-x on the following intervals. (a) (-3,0] (b) [-3,3]...

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Q: Evaluate log, 99

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

Q: Q8 Determine whether {(1+2)"} Converges or diverges. n=0

A: To find the convergence of 1+pnpnn=0∞ For that, note that: limx→∞1+axxa=e

Q: If a1, a2, a3, ..... , an are in AP witn common difference d (where d + 0) then the sum of series : ...

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Q: The graph of a function of the form f(x) = ax + bx +c for different values of a, b, and c is given. ...

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Q: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2x). (Enter your answe...

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

Q: In one of the warehouses of a construction firm, cement is being released from an elevated storage b...

A: Given: Cement is being released from an elevated storage bin at a rate of 29 feet3/min. i.e. dVdt=29...

Q: Use linear approximation to estimate the following quantity. Choose a value of a to produce a small ...

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Q: Consider the following. u = (3, 7), v = (4, 6) %3D (a) Find the projection of u onto v. 27 13 (b) Fi...

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Q: Prove the identity. (Recall sinh(a + b) = sinh(a) cosh(b) + cosh(a) sinh(b).) sinh(2x) = 2 sinh(x) c...

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Q: 2 y = 2x – x¯, y=2x¯ – 4x

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Q: Find the angle 0 between the vectors in radians and in degrees. u = 9i + 5j + k v = 5i - 9j (a) radi...

A: In this question, we need to find the angle θ between the given two vectors.

Q: 4. Solve the linear system below w + x - 4z = -2 0.5w – 0.5x + 2y + 0.5z = –2 -3x + 0.5y + z = -5 4w...

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Q: Consider the following planes. 5x + 6y – z = 66 x - 12y + 2z = 0 (a) Find the angle between the two ...

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Q: Let the function f be defined by tan(x) - 1 f(x) = sec(x) (a) Use the Quotient Rule to differentiate...

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

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Q: x arctan xdx

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Q: In a circle, a central angle of 2.5 radians intercepts an arc of 15 inches. Find the number of inche...

A: Given:   Angle ( θ ) = 2.5 radians     Arc length (S) = 15 inches  

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. X = 4t, y = 4 –...

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Q: 2. Derive the Maclaurin series for cos-(5x) as far as the term in x. Hence evaluate cos (1) to 4 sig...

A: Let's find.