Determine whether the vector field is conservative. F(x, y) = xe(x^2)3y(2yi + xj)   If it is, find a potential function for the vector field.      _______+ k

Q: Find the area bounded by the given curves. ')y=x3, y=x2

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Q: 3. y + 4y'+4y=0

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Q: Find y' and the slope of the tangent line to the graph of (3x - 5y)5 = 2y2-9 at the point (3,2).…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the given…

Q: Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1. (A) 3.68 square units; (B)…

A: The region is bounded by the curves y=ex, y=x2-1, x=-1 and x=1

Q: II. Solve each of the given LDE of order n. 2. (D³ +6D³ +2D² - 27D+18)y=0

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Q: One type of strontium has a radioactive decay rate of 1.4% per day. If 30 pounds of this strontium…

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Q: If the function f(x) is a quadratic function, then f(x) must open x-intercept(s). and have ii The…

A: If function f(x) is a quadratic equation, Then f(x) changes direction once.

Q: b) [ bounded 1: Find the volume of the solid obtained by rotating the region by the curve about the…

A: Graph:

Q: (a) Use midpoint rule and trapezoidal rule with n = 5 to approximate the following integra- tion…

A: Given :∫-23x2dx    ,n=5

Q: 1)Determine the equation of the tangent line to the intersection of the surfaces x²-y=0 and y+z²=16…

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Q: Find the absolute minimum and absolute maximum values off on the given interval. f(t)=t√ 25-t²,…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) làm 9 cot x

A: topic- limits

Q: 3. State the remainder when f(x) = 2x² −x³ +1 is divided by (x+1).

A: We can find the remainder as below.

Q: 2. Find the radius and interval of convergence for the series. (x - 2)" nn n=1

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Q: f(x)=3x²-x+2,a=1 f(x)=6

A: Solution of given question is written in below steps.

Q: Find y' and the slope of the tangent line to the graph of (3x-2y)5 = 2y2-9 at the point (1,2). y'=0…

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Q: n=0 In(n + 4) n+4

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Q: dx Assume that x = x(t) and y = y(t). Let y = x³ +5 and dt Find dy dt dt when x = 3. (Simplify your…

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Q: Given that n=0 x = 1 1-x Identify its interval of convergence. The series is convergent from , left…

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Q: State the equation of the oblique asymptote of the function g(x) = 4x² +5x+2 x + 2

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Q: Your answer is correct. Find the solution of the given initial value problem in explicit form. ) =…

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Q: Determine any planes that are parallel or identical. (Select all that apply.) P₁-120x +90y + 120z =…

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Q: (ii) Find all values of k for which the integral fo (+)da converges and evaluate the integral at…

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Q: If I have a continuous, smooth (no sharp points) function with 3 local maxima and 2 local minima,…

A: Since the function is continuous , with 3 local maxima and 2 local minima.the function will have 5…

Q: For f(x, y) = cos(xy²), which of the followings is true? O fr = fy O fxy = fyx O frr = fyy O fryr =…

A: The given function is fx,y=cosxy2

Q: Question 5 Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis.

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Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 ≤ 0 <…

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Q: Find the exact solution for e2-6e* If there is no solution, enter NA. 160. Enclose arguments of…

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Q: If v=4i -Ĵ+3k and w= -î - 2 + 5k, then find the dot product, .W 11 13 10 11 8

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Q: Match the graph of the above function with the graph of its derivative. 0 ㅇ O 수 +

A: The given graph of the function is the graph of a semi circle. Or positive side of the circle.

Q: Laplace Transforms. 1. Determine the Laplace Transform of the following functions: a. f(t) = 5te-t +…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 2. X-4 8x-7 f(x) =…

A: We can solve this as follows:

Q: Consider the following function and graph. f(x) = x + 2 1 -3+ Determine whether f(x) approaches ∞ or…

A: In this question, we want to find the left hand limit and right hand limit of the function.

Q: [x³e'dx,

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Q: F(x, y) = (3x-4y2i+6yj by the force in moving a particle in the positive direction once around the…

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Q: Find the derivative of f(x) = = 4√√x + 2 x7 . Type your answer without fractional or negative…

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Q: What is the antiderative of xysin((x^2)y)?

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer…

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Q: 1. Which of the following values would be obtained using 10 circumscribed rectangles of equal width…

A: The integral is  ∫01 x2 dx

Q: If sin x = sin(2x) cos(2x) tan (2x) 3 7' x in quadrant I, then find (without finding x)

A: NOTE: Refresh your page if you can't see any equations. . here we have  and the angle is in the…

Q: Consider the following function and its graph. f(x): X x² + (b) Use the graph to determine the limit…

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Q: Describe the Interval(s) on which the function is continuous. (Enter your answer using interval…

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Q: 13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3-2 Find an equation for the graph above. 5+ g(u) 4 3 2 - -2- -3-…

A: We need to find equation of given graph.

Q: Without using a calculator, find the distance traveled by a particle with position (x, y) as t…

A: The distance travelled by the particle is the same as the arc length as varies within the interval…

Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

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Q: csc(x) = 5, for 90° < x < 180°, then (²3 2

A: Please refer to the image below

Q: C'(x) = C'(8) = 1 √√2x + 48

A: It is given that, C(x)=7+2x+48     ,    0≤x≤50 We have to find the value of C'(8).

Q: Consider the following. f(x) = 81 Find the x-values (if any) at which f is not continuous. Is the…

A: We know that discontinuity is a point where the function becomes undefined. The point of…

Q: What is the integral that represents the length of the curve from x = 2 to x = 4. Select one: 0 ₂²…

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Q: Given f(x)=√x and g(x)=x²-1, evaluate each expression. (a) f(g(1)) (b) g((1)) (c) g((o))

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