Determine whether the alternating series converges. 4ln k E(- 1)* k k=3 O The series diverges. O The series converges.

Q: 3. Sketch the graph of the derivative of the function below.

A: A rough graph can be plotted as values are not given in the given graph

Q: (Don't forget to include the constant of da x + 3 antidifferentiation C) Evaluate

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Q: Find 02/ay and az az 02/ax of the following function: z = x³ev* + y5 In(2x + y)

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Q: The magnitude of three vectors a, b, and c form a right triangle. Given the equation, what is the va...

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Q: The region bounded by f(x) = - 1la + 6x + 27, a = 0, and y 0 is rotated about the y-axis. Find %3D %...

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Q: Find an equation of the tangent line to the curve at the given point. y = (1 + 3x)1, (0, 1)

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Q: If f(t) = (t + 7t + 3) (5t? + 4), find f'(t). %3D Find f'(1).

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Q: lim (-4 0 sin x x

A: Let ,I=limx→ 01sinx-1xTaking cross multilplicationI=limx→ 0x-sinxxsinxI=0-sin(0)0sin(0)I=00Which is ...

Q: 05+-06 dt .07

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Q: After school, Shaquille and Reyna need to pick up their basketball uniforms and return to school for...

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Q: (0, 1) (0,0) (1,0) FIGURE 0.1. The triangle T of the problem. Consider the triangle T with vertices ...

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Q: Find a bound for the error in the approximation M10 to the given integral (but do not calculate M10)...

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Q: 9. (b + 4)e db

A: This question is based on Indefinite integration.

Q: Discuss the continuity of the function: (x2 + 2x - 4 xs-2 g(x) = } (6– x) x > -2

A: Given :g(x)=x2+2x-4x≤-2(6-x)xx>-2

Q: If 0° < 0S 360°, find all the angle measures of 0 that makes sec 0 = -V2 and Ssc e = V2.

A: Given,           secθ=-2 and cscθ=2To find : The measures of all angle, θ.

Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5-3x at x = 1. What is y(2)?

A: This question is related to differential equations and straight line, we will solve it using given i...

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (– 1)* Σ k=I V...

A: The given series,       ∑k=1∞(-1)k6k(k+1)

Q: If f and g are continuous function of X, which of the following is true? )dx =D| (x) dx B dx3D 8(x) ...

A: Given :

Q: Find the differential of each function. (a) y = etan(nt) %3D dy = te tan (Tt)sec?(rt) 2. secʻ(nt) (b...

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Q: d/dx[(x2 + 5)(x³ - 7) = 5x4 -15x2 + 14x Select one: O True O False 1 1 d/dx(I + Select one: O True O...

A: See the details solution in below

Q: Find the volume of the region under the surface z = I+y = 6 1680zy and above the area bounded by z =...

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Q: If F is a continuous on the set of real numbers, then (A True (B False

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Q: boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on...

A: topic - application of derivatives

Q: d²y 4 + y = t2 –- 2t + 3 dy - dt2 dt

A: As per the guidelines, are supposed to solve only one problem, please re-post the other problems ind...

Q: Indefinite integral (1/((x^2)-6x+b)dx How could I calculate the b value using u-substitution and the...

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Q: From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an...

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Q: To test this series for convergence n2 + 1 n=1 n' + 6 You could use the Limit Comparison Test, compa...

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Q: Choose the type of the conic section. O hyperbola O parabola

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Q: Determine the exact coordinate of a point at a distance of 4 units from the origin in the second qua...

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: Consider the conservative vector field F(r, y, z) = (2x, z, y). a) Determine a potential f such that...

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Q: A closed cylindrical tank of circular cross-section has a radius of 2 ft. and a height of 6 ft. Use ...

A: Radius = 2 ft Height = 6 ft dr = 1 inchdr =112 ftdh = 1 + 1 (top+bottom)dh = 2 inchdh = 212 ft

Q: 9. Reduce the following equation to one of the standard forms, classify the surface, then sketch the...

A: General equation of an ellipsoid is given by, (x-p)²/a² +(y-q)²/b² +(z-r)²/c²= 1

Q: Verify each differentiation formula d -u (a) [Arccos(u)] = dx V1-u? (b)(Arccot(u)] = d -u dx 1+u² -u...

A: As per the instruction, we will be answering the first one. For (1), For (a), arccosu' =-11-u2×u'   ...

Q: Calculate the integral: dx J (e² – 4)(e* + 6)

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Q: A painting contractor charges Php 120 per sq.m. for painting the four walls and ceiling of a room. I...

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Q: Find मिव x) e -e e* + eX

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Q: Find 6z - 5/T + Type your answer without fractional or negative exponents. Use sqrt(x) forsqrt(x).

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Q: 1. The function f(x) = 81 has a discontinuity at x = 9. 2. The function g(t) = |2x – 10| has a at r ...

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost oth...

Q: Suppose f (x, y, z) =D 를+끝, P= (1,2,4). A. Find the gradient of f. Vf * i+ j+ k Note: Your answers s...

A: Given :f(x,y,z)=xy+yz, P=(1,2,4)To find :  The gradient of f and the maximum rate of change of fat t...

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x'-5x)* 1. y= d'y/dx'

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Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (1, -4) and the direction in w...

A: Here, the given function is: f(x,y)=ln(x2+y2)

Q: f(t) = e-5t

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Q: &r4- V Let y=f (x) + C be the antiderivative of F (x) = determine the value of C (use 3 decimal plac...

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Q: Sketch the graph of the function g for which g(0) = g(2) = g(4) = 0 g'(1) = g'(3) = 0, gʻ(0) = g'(4)...

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Q: your a ;) lim x4+メーLo メ→。 i) lim 左十 \im tメーLo X→-∞ iii) \m 4a(a+)しメー2)しメ+ム) メ→ ○

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide ...

Q: Solve the given differential equation. x2y" + 13xy' + 36y = 0 y(x) = ,x > 0

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Q: Solve the following DE subject to given conditions, using Separable method. 2. y' (x+2)+4x(y +2y+1)=...

A: Separable differential equation can be written in the form dydx = f(x) g(y). ∫ax+bn dx = 1a.ax+bn+1n...

Q: Stan (y-t0) dy ( α年

A: Our Aim is to evaluate the integral given below:-∫tan y-π4 dy-(i)

Q: Express the repeating decimal as a fraction. 1.959595...

A: Topic:- algebra