1-2n The sum of the series 1 is: A) 1. B) 2. C) D) E) Diverges.

Q: Determine whether the series converges; if so, find its sum. Otherwise type N in the blank. 1 k(k + ...

A: Given Series ∑k=1∞ 1kk+2  

Q: 4. Given: a, = 5, a4 = 13 Find: d =? а. 1 b. 2 с. 3 d. 4

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Q: What is the value of 1/2 x(3 cos(x) + sin(x))dx ? -7/2 Give your answer as an integer or as a decima...

A: Topic:- integration

Q: Solve the following differential equation dy _ x²+y² dx ху Select one: O a. y? = x?Inc²x² O b. y? = ...

A: Solving by exact differential equations

Q: (2х — Зу + 2)dx - (3x + 4у-5); У-3) %3 4 |

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Q: Evaluate the integral. 5 x2 e dx +C

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Q: The owner of a cattle ranch would like to fence in a rectangular area of 3000000 m² and then divide ...

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Q: Solve using the U-Technique Question 8 Given: S . There is a function f (x) such that when u = -x³, ...

A: Given: ∫2f(x)dxe-x3   , u=-x3

Q: Determine whether the alternating series converges. 11ln k (- 1)*. =3 k O The series diverges. O The...

A: In this question we have to find the whether the series is converges or diverges.

Q: A statue 3 m high is standing on a base of 4 m high. If an observer's eye is 1.5 m above the ground,...

A: Solution is written in below steps.

Q: What is the value of 7/2 x(3 cos(x) + sin(x))dx ? 7/2 Give your answer as an integer or as a decimal...

A: Given I=∫-π2π2x(3cos(x)+sin(x)) dx To evaluate the Integral I :

Q: If we let u = 4x – 1 for theS 2 tan(4x-1)-3 cos² (4x-1) dx, what will be the resulting integrand? co...

A: Solving the problem by finding the integrand.

Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

A: Let length of one piece be x, then the length of the other piece will be 48−x.

Q: Find the derivative of y with respect to x for y = sinh 1(11/15x). dy 165 dx 2/1815x? + 15x

A: Given query is to find the derivative of the expression.

Q: Determine whether the alternating series converges. 51n k | k k=3 O The series converges. O The seri...

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Q: Use the given definition to find f(A): If f(x) = a, + a,x a,x + ... + ax" is a polynomial function, ...

A: This is a problem related to matrix. We will find out square of the matrix and then calculate f(A) m...

Q: Find the equation of a NORMAL LINE in SLOPE-INTERCEPT FORM to the given cu below f (æ) = (x² + 1)* %...

A: Note: The normal line is defined as the line that is perpendicular to the tangent line at the point ...

Q: y = cje + c2er

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Q: (x – h)? + y? = r² O y " +(y')² + 1 = 0 O y" +(y')² = 0

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Q: For the following primitives, identify the number of essential constants.(x and y are the variables)...

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Q: Evaluate the double integral Jo J-y? dxdy

A: To evaluate: ∫02∫-4-y20dx dy

Q: solve for x the equation 4y = 3x2 + 2x – - 5

A: The given equation,     4y=3x2+2x-5

Q: 3. Is the function given by Sx-4x-5, メ<5 X-5 2. continccus at x =52 Why ar whynot ?

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Q: If cotx 12 find the other trigonometric functions

A: topic - trigonometric ratios

Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

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Q: Does the following set of order pairs represent a function? If so, does it represent a one-to-one fu...

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Q: Find the particular antiderivative that satisfies the following conditions: 10 10 H' (x) x2 ; Н(1) —...

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Q: Evaluate the integral. |a cos(6 z) dz =| %3D

A: Topic:- integration

Q: Evaluate the following integral. Sesim (5- In 2 dx 3

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Q: 5. if we have two polynomials pl=3x5 + 8x* – 2x2 + 4x + 1 p2= 2x6 + 3x* – x² + 4x Find:- Your answer...

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Q: find the function y(x) satisfying dx/dy=5x ^(-6/7) and y(-1)=-2

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Q: H.W Find the Adjoint to the following matrix 0.5 01 X = -1 1 -0.8 2.2 2 -3.3

A: Let A =[ aij ] be a square matrix of order n. The adjoint of a matrix A is the transpose of the cofa...

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t аnd x = sec-1 t

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Q: The function f(x, y) : 1+2? +y? is 1-x2 -y? discontinuous at the points {(x, y)\æ² + y² # 1}. True F...

A: f(x,y)=(1+x^2+y^2)/(1-x^2-y^2)

Q: equations

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Q: If u = f(x), then S k dx = +C for some constant k. Compute kf(1). %3D x*+2x2+1 x2+1 4 -1

A: u=f(x)f(x)=xx2+2I=∫ xx4+2x2+1 dxI=∫ x dx(x2+1)2u=x2+1du = 2x dxx dx =du2

Q: Find the differential equation whose solution is given by: y^2=4ax

A: To find the differential equation for               y2 = 4ax differentiate this equation with respec...

Q: Evaluate O a. 2/ + 3+ 3-6ln |z/+1|+C O b. 2 3T+ 32 +6ln r/ +1+C O c. 2vE - 3T +322 – 6ln |z'/0 – 1|+...

A: ∫1x+x3dx

Q: Problem 1: An open rectangular box is to be constructed by cutting square corners out of a piece of ...

A: Given dimensions: The dimensions of the cardboard are 14cm×12cm An open rectangular box is to be con...

Q: Let J ex+1 S dx be given . If u = e* + 1, then the resulting integral is S f(u) du. Compute f(3).

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Q: Evaluate the following differential equations by method of variable separable. Show your solution. 1...

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Q: Evaluate the integral. x sec (3x) dx = +C

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Q: 2. Given: a, = 5, a4 = 14 Find: az =? а. 7 b. 8 с. 10 d. 12

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Q: W= x"+y+Z",

A: This is a problem of partial differentiation. Based on the general formula of PDE we will solve the ...

Q: u+1 Using u-substitution, the integral S f(x)dx reduces to a new integral f g(u)du. If g(u) evaluate...

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Q: Solve using the U-Technique Question 12 Consider ) x(1+v) dx and using u-substitution in rewriting t...

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Q: du The integral S- reduces to S k, where u = f(x) and for some constant k . Compute f(1). e*+1 e +1 ...

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Q: 8. Show your complete and step by-step solution. dx 6. Evaluate – 16r? 2e" 7. Evaluate +4e'+6 8 Eval...

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Q: e solution to fe2* sec?(e2x+1)dx is equal to k tan(e2*+1) + C , find the exact value of k.

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

Q: Consider dx and using u-substitution in rewriting the integrand as a function of u and du . x(1+vx) ...

A: