- 2y : Sketch in one coordinate plane the circies 2x – 6y + 6 = 0. Then, find their points of intersection.

Q: Use sigma notation to write the Maclaurin series for the function 11 In(1 + x)

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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: 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: Determine whether the series converges, amd if so find its sum. If the series diverges, indicate tha...

A: Topic:- sequence and series

Q: For the following function ds find the antiderivative s that satisfies the given condition. dt ds -=...

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Q: 2. (x +1)y'+y = x² – 1 %3D -

A: Topic = Differential equation

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

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Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

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Q: Find the Taylor polynomials of orders n = 0,1, 2, 3, and 4 about a = x0 |and then find the nth Taylo...

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Q: Using the partial fractions technique, the function f(x) = 37x+82 can be written as a sum of partial...

A: ∫37x+82x2+2x-24 dxConsider 37x+82x2+2x-2437x+82x2+2x-24=37x+82(x-4)(x+6)37x+82(x-4)(x+6)=Ax-4+Bx+637...

Q: Required information NOTE This is a multi-part question Once an answer is submitted, you will be una...

A: Here we have to find B*B*B. Where B ={x.y}

Q: Solve using the U-Technique Question 18 dx du The integral S; reduces to f ka", where u = f(x) and f...

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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: Given: S 5x? cos 3x³dx. If u = 3x³, then the resulting integral is S f(u)du. Find f ():-- 5/7 A 2 5/...

A: topic - functions and indefinite integral

Q: What is the slope of the NORMAL LINE to the given curve y = x + at point where x = 3 *If the answer ...

A: The given function is; y=x +1/x at x=3.

Q: 2. Show your solution. The sample space that describes all three-child families according to the gen...

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Q: Consider the expression ſ V4 – x² dx = F(x)+C. The expression %3D F(2) – F(-2) is equal to

A: Here we have to evaluate F(2)-F(-2)=? We have, ∫4-x2dx=F(x)+C

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

A: As we know that the nth order Taylor's polynomials at x=x0 is given by; pn=fx0+x-x011!f'x0+x-x022!f'...

Q: Evaluate Log base (1-i) (1+(sqrt of 3)i) and express the final answer in polar form.

A: Given: - log(1-i)(1+3i) To evaluate: - The final answer in polar form.

Q: 2. (x + 2) dæ: (x + 3) sin y cos y dy In(a + 3) sin y %3D + C ans. x -

A: (x+2) dx = (x+3) sin y cos y dyUsing the method of variable separable;x+2x+3 dx = sin y cos y dy   ∫...

Q: (y² + x²y + 2x)dx + (x³ + xv+ 1)dy= 0; y(2) = -3 %3D

A: Given: y2+x2y+2xdx+x3+xy+1dy=0, y2=-3 We have to find the particular solution.

Q: The integral / 2' )cos(2*) dx takes the form k cosu du when u=2* and f (x) =x- 5. What is the value ...

A: we use the formula ddx(ax)=ax lna

Q: The integral / 2/ ) cos(2*) dr takes the form & cosu du when u=2* and f (x) =x-5, What is the value ...

A: Firstly We have to solve the integration, then compare to given form and find k. Then We get K+2.

Q: 2. Given: a1 16, а4 1024 Find: az =? а. 12 b. 18 с. 36 d. 64

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Q: Solve the initial value problem for x as a function of t.. dx (? - 15t + 56). = 1 for (t> 8), x(9) =...

A: Given that      (t2-15t+56)(dx/dt) = 1 for (t>8), x(9)=0 Here we have to find the initial value p...

Q: Find the equation of the tangent line to the curve given by y. Sin (z) + e² - Tan (y – 1) = 0 a the ...

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Q: 2.ly-x dx+ dy = 0

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Q: For ſ k*e3* dx = 1 (ke)3x 3 (1–In 2-1) + C. If u = 3x, then k =?

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Q: Evaluate the integral using tabular integration by parts. 4 x V2 x +1 dx +C %3D

A: LetI=∫ 4x32x+1dxPut 2x+1=u2x=u-1x=u-12differentiate 2dx=dudx=du2I=∫ 4u-123udu2I=∫ 4u-138udu2I=∫ 14u-...

Q: Use integrating factors to solve (x² + y² + x)dx + xydy = 0. %3D

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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

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Q: Solve the system of linear equations given below. -11х1 + 13х2 — 15хз + 25х4 %3D 101 -19x1 + 33x2 + ...

A: Here is the solution

Q: cosx * sin? (3x) 2 2. lim x→0 x2

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

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Q: Question 16 Determine f(x) so that | cos(In?x) f (x) dx = sin(In²x) + C ... 2ln(x) A) In(x) B 2In(x)...

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Q: 12. Evaluate ((1– cos x) dx a.) 1- sin x +C b.)x - cos x +C c.) 1- cos x+C d.) x- sin x+C 13. Evalua...

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Q: prove that tanx = V secxsinxtanx %3D

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Q: If the solution to fez* sec²(e2x+1)dx is equal to k tan(e2*+1) + C , find the exact value of k:.

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Q: A. 5x + 6+ 4x

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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: Question 2 If S(16x4 – 16x³ + 4x²)dx = F(x) + C, then F(x) 16 A 5 4 x3+4x4 3 B (4x² – 2x) 3 16 4 x3 ...

A: The given integral is 16x4-16x3+4x2.

Q: If g(x) = f'(x) and if g(x) = (cos x – x sin x)e*cosx, then S g(x) tan(f(x))dx is x cos x

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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...

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Q: Find the particular antiderivative that satisfies the following conditions: dR 20 R(1) = 50. dt t2 R...

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Q: 1+ In x Find f (x) so that when u = f(x) the integral dx can be rewritten as cot u du . I tan(f(x))

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Q: Which of the following is true about horizontal asymptotes? OAll rational functions have at least on...

A: Find your answer below 

Q: k If u = f(x), then f dx x4+2x²+1 +C for some constant k . Compute kf(1). x2+1

A: topic - functions and indefinite integral

Q: If the solution to ſe2* sec²(e2*+1)dx is equal to k tan(e2x+1) + C , find the exact value of k... 1 ...

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Q: 12 1. Given that sine and 0 < 0 <", find sin(20) and cos(20) 13'

A: We know in the first quadrant that is 0&lt;θ&lt;π2 both sin and cos take positive values. cos(θ)=±1-...