ex V1-e2x 1. S dx

Q: 6 Use substitution to find the Taylor series at x = 0 of the function 1-9x 6 What is the general…

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Q: Differentiate the following function. f(x) = (x+2) e-6x +1 f'(x) = (Type your answer in factored…

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Q: lo 3 Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar…

A: Let's change given Cartesian integral to polar integral and then evaluate.

Q: y" + y = 3x sin x

A:

Q: Find the triple integral of the function f(x, y, z) = x³ cos(y+z) over the cube 3 ≤ x ≤6,0 ≤ y ≤ m,…

A: ∫36∫0π∫0π   x3cosy+zdzdydx

Q: 1–2 = For each of the following functions given by power series, find f'(x) and f f(x) dx. Do not…

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Q: 5. y³ = 4(y + x²)

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Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y² =25 and…

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Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

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Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

A: Given problem:- Evaluate the ∫∫∫E z dV, where E is bounded by the cylinder y2+z2=4 and the planes z…

Q: 5. Find the average value of f(x) = 1 X on [e4, e5].

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Q: If f(x) = x'ex, find f'(x) and f'(1).

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Q: Determine whether the following function is differentiable at x = 9 f(x)=√x²-16, x<9 √x, x ≥9 (a)…

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Q: Evaluate the triple integral edV where E is bounded by the parabolic cylinder z = 1 - y² and the…

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Q: Find two polar coordinate representations for the rectangular coordinate point (-√2, √6), one with…

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Q: 2. Use geometry to evaluate (2 (2x+6)dx. You need to draw a graph.

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Q: What are the vertices of the hyperbola whose equation is: * 9x² -4y² +72x + 108 = 0 (-1,0) and…

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Q: 51 1. A parabola with directrix y = == 32 and one endpoint of the latus rectum at nat (-²,-2)

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Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=-3x²-3xy-8y²…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: Find at least 5 distinct rational points on the unit circle in the first quadrant of the plane.

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Q: Find the average rate of change of the function over the given interval. f(t) = 13+ sint a. 0, 플] п…

A: As we know that; The average rate of change between the interval t1≤t≤t2 is given by: Average rate…

Q: What is the area of the region between X |y=x2–2x−3 and the x-axis from x=0 to x=4?

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Q: Q2/Find the value of the integral fx by using simpson method (n = 6)?

A: This is a problem related to integration using numerical method. Based on the general formula of…

Q: Definite

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Q: Determine the intervals on which the function is concave up or down and find the points of…

A: solution:-f(x)=6x3-11x2+1f'(x)=ddx6x3-11x2+1=18x2-22xf''(x)=d2dx26x3-11x2+1=36x-22

Q: We know that for some real number k, the function 3ekx is the solution of the second- order…

A: This question can be solved by substituting the value of y in the given differential equation.

Q: Q2/Find the value of the integral dx 1+x² by using simpson method (n = 6)? 3

A: Find out the value of the integral using the simpson 1/3 method.

Q: Consider the matrices shown below: Compute CT-A 3 07 A = -1 2 E -B C = 13] 3 1 5

A: Given: A=30-1211, C=142315

Q: 8. Consider an object moving along a line with velocity v(t) = 6t2 - 12t with t measured in seconds…

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Q: 2. 8 2 + (-1) 5+

A: Here we have ∑k=1∞2+(-1)k5k

Q: (CLO-3) Find the area of the largest rectangle that can be inscribed in the region enclosed by the…

A: Given:-y=x2-5y=-x2+5let x=t  and -t are paramatric points on the curveboth the curves are…

Q: Determine the intervals on which f is increasing or decreasing, assuming that given figure is the…

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Q: R 쫘 = 0.138 & R" . R₁ " 0.126

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Q: Ут. У 4+ 2 ly мв a.

A: The given series,       ∑k=1∞2k4+k

Q: (y² - 2xy + 6x) dx - (x² - 2xy + 2)dy - 0

A: We have to find out solutions

Q: Evaluate the triple integral a dV where E is the solid bounded by the paraboloid a = 10y² + 102² and…

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Q: Solution 1 y = (x + 3)(2x − 5) y = 2x² + 6x - 5x - 15 y = 2x2 + x – 15 y = 2(2x)2-1+1-0 y' = 4x+1…

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Q: 4 √25-x² X 3 dx

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Q: 2. S dx x²-x+2

A: Given problem:-

Q: Find the point on the plane 5x + 4y + z = 11 that is nearest the origin. What are the values of x,…

A: First we find the distance(d) between a point (x,y,z) on the plane and the origin .Then form a…

Q: Q1): Prove that: A square matrix B has inverse if and only if determinant of B is not equal zero.

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Q: S x dx √16-9x4

A: Topic = Integration

Q: 2 Let f(x) = 5x4 -/+8√x-3. a) Find f'(x). (b) Find an equation for the tangent line to the graph of…

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Q: 3. Let R be the region below bounded by the parabola y = 4 – x² and the lines 3x - 2y + 3 = 0 and y…

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Q: X₁ = (-1, -2) & (3, 1) Y₁ = ; X2 = m m Final answer: Trend: || Y2 =

A: Slope of a line is = y2-y1x2-x1If the slope is positive then the trend is that as x increases y…

Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) =…

A: The quadratic and cubic approximation at (0,0) formulas are:…

Q: Identify

A: Please refer to the image below