Q) Test the convergence and divergence of the following series using ratio or root test 3n ∞ 1) Σ =o n=0 n³2n

Q: The exact value of sec 2√3 3 0-2 2√√3 3 c (55) ₁ is 6 02

A: Use trigonometric coordinate syste

Q: √10-x² x = √10 sine x = √10 cote 15. What trigonometric substitution can be used to evaluate a. x =…

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Q: Calculate 14. lim (√x² + 1 - x). X18

A: Using series expansion about x =inf

Q: Explain why the calculation (axb). (ĉ. d) is not meaningful.

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Q: D) Find the parametric and symmetric equations of the line through the points (1,2,0) fic and sym of…

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Q: Nx - My M If = Q, where is a function of y only, then the differential equation M + Ny' = 0 has an…

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Q: Find the Laplace or Inverse Laplace of the following as indicated 4s+12 1. s²+85+16

A: We have to find inverse Laplace

Q: 3. In 2 et e²x + 4e²+ 13. dx

A: definite inegration

Q: Question 2 Find two numbers whose sum is "a", if the product of one by the cube of the other is to…

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Q: 1 -dx 1-x²

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Q: Example 4: Find the equation of the plane through the point (-4, 3, 1) that is perpendicular the…

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Q: 13. Given - 5x + 5z = a. (-5, 5, 2) 2, the normal of the plane is: b. (7, 7, 0) c. (-5, 0, 5) d.…

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Q: The power series n=1 0-1≤ x < 5 01≤x≤5 0-1 < x < 5 0-1≤x≤5 (x - 2)" 3n converges if

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Q: 8. Evaluate: fdx a. x + x+In+C b. In(x²-1) + C C. x + tan ¹x + C d. 1+In+C x-1

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Q: 5- The tail of vectors a and b form two sides of a parallelogram. Vectors is 30 degrees, and the…

A: Area of a parallelogram when two sides of the parallelogram are given by the vector a→ and b→ is…

Q: Q2: Find a general solution of the differential equation (D² + 6D +13)y= 10e³- 16e using the…

A: Concept: The general solution of the given differential equation is given by  y=C.F+P.I Here C.F is…

Q: nd an equation of the tangent plane to the given surface at the specified point. z = 4x² - y² + 4y,…

A: Topic:- application of derivatives

Q: 1. what is the basic concept of a derivative? How is this derivat calculated? What techniques/ have…

A: Topic:- calculus

Q: 1. Given the function f(x)=2-4x+ +$. Please find the intervals of increase or decrease, absolute…

A: Given problem:-

Q: ata Careek. The following expression represents the Riemann sum, sing over some interval [a, b], a…

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Q: Expand f(x) = 3x as a half range Fourie.....sine.... series in the range 0.₁FX.. F... ..ans.: f(x) =…

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Q: You want to travel from point A to point D at the fastest possible time. You can walk faster along…

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Q: Find the area of the largest rectangle that can be inscribed in a circle of radius 20 cm. Answer:…

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Q: 4) The student population at a certain school here in Dagupan can be modeled by the logistic growth…

A: You must have idea about growth model to understand it better.

Q: Choice

A: Please refer to the image below

Q: 10) In an aquaculture, the amount of bacteria doubles every 7 minutes. If the amount of bacteria…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: vergence of the following power series Find the radius of conver E n+ 1x² 41 n=0

A: We have to find the radius of convergence of the power series ∑n=0∞ n+1n2+1 xn.

Q: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: Solve for the value of “C” on the given differential equation below. Let y(1)=1 ( 1y – x2 )dx + xdy…

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Q: Find the area of the shaded region. y=2x2+x-6 y=x2-4 W

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Q: 3. Find the intersection of the following planes: ( x - 3y - 2z =- 9 == 2x - 5y + z = 3 3x + 6y + 2z…

A: We have to find the intersection of 3 planes.

Q: Nx - My If = R, where R is a function depending only on the quantity z = xy, then the differential…

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Q: NOTE: Enter the exact answer. [11x + ]dx = 7 8x³ +C

A: Using given rules evaluate the integral following

Q: (2x5-x3-1)dx x³ - 4x

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Q: Find the volume of the solid generated by revolving the region about the given line. The region in…

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Q: 2) A bacteria culture which started at 2, 000 became 6, 000 after 4 hours. After how many hours will…

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Q: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: Evaluate lim x tan a x - x cos x

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Q: Define the binary operation in the set of rational numbers as: a*b = ab + a-b Which of the following…

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Q: Calculate lim X10 3x²-x-2 5x² + 4x + 1

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Q: Problem 7. Find absolute extreme values for f(x) = ³ − 6x² + 5, x € [1,5].

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Q: 1. Evaluate the dy for parametric equations x = 3t³ - 3 and dx y = 3t² - 6t using parametric…

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Q: Determine whether the equation is exact. If it is exact, find the solution. 3 2eycosy + = C 2. 3…

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Q: Solve for y esec(4y²-6y+14) = 3x + 1

A: To find the value of y , first, we take the logarithm on both sides of the given equation and then…

Q: 4. The point (0.422,-0.907) lies at the intersection of the unit circle and the terminal arm of an…

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Q: 5- Determine the value for x such that the points A(-1,3,4),B(-2,3,-1), and c(-5,6,x) all line on a…

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Q: A lighthouse is located on a small island 4 km away from the nearest point P on a straight…

A: Given problem:- A lighthouse is located on a small island 4 km away from the nearest point P on a…

Q: -x-7 fres-2 [F(x)= x² for-2 2 At x = -2 because limit as x approaches -2 of f(x) Does Not Exist At x…

A: Topic:- calculus

Q: Solve for y esec(4y²-6y+14) = 3x + 1

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Q: (x + ex sin y) dx - (y + e-x cos y) dy = 0

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