Give the equation of the normal line the graph of sin" (x³) + (log3 y) 3 aut le 1)

Q: Often a differential equation with variable coefficients, y" + p(t)y' + q(t)y = 0 (i), can be transf...

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A: The orthogonal projection of a vector a→ onto a vector b→ is calculated using the formula: orthb→a→=...

Q: The P-test says that: 1 • the series ) converges if p( ? 81 kP k=1 1 • the series diverges if p ? 0 ...

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Q: Evaluate the integral: fa°/25 – 2°dz (A) Which trig substitution is correct for this integral? Oz = ...

A: The derivative of a function y=f(x) is the measure of the rate of y with respect to x. According to ...

Q: In Exercises 37-40, specify the boundary and the interior of the sets S in 3-space whose points (x, ...

A: Given:the boundary and the interior of the sets S in 3-space whose points (x, y, z)  

Q: Integrate the function f (z) = (z – 8i)? from z = 0 to z = 4 + 4i along the line x = y.

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Q: Let 0 0 -1 1 0 1 A = %3D | 0 1 (a) Find all eigenvalues with their multiplicities. (b) Find the defe...

A: We can solve this using given information

Q: 1. Let R be the relation on N defined by "aRb if EN or 5| (b- a)". So for example (6, 2) € R and (1,...

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Q: Consider the nonhomogeneous system X': Find a fundamental matrix 4(t) for the associated homogeneous...

A: We will use the basic knowledge of ordinary differential calculus and linear algebra to answer this ...

Q: 8. If the equation Ax = b has more than one solution for some b in R", then the columns of A span R"...

A: This is a problem of linear transformation.

Q: Find the volume of the solid generated of the area bounded by y = x², y + 2x = 8 and y = 0, rotated ...

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Q: Find the graph of this arclength

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Q: Exercise 4. Let F and G be homothetic functions in two variables. Is their sum homothetic? [Hint, st...

A: We will use the fact that the MRS of a homothetic function is always homogeneous of degree 0.

Q: - - 2. Find the general solution to the differential equation y(4) – 7y(2) + 10y' – 4 = 0.

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Q: Evaluate the moment M, and My of the region bounded by y = 2x + 1, x + y = 7 and x = 8.

A: given curves y=2x+1 , x+y=7 , x=8 evaluate the moment Mx and My of the region 

Q: dy ,2,,2 1. х + 3y = x?y? dx

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Q: 3 4 S 2. 4 4 2 2 - 4 3 2 A = 4 3 3 4 2 - 4 - 2 2 2 2 3 4 3 + 2 2 3. 2.

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Q: Find the volume of the solid generated by revolving the area bounded by x² – 2kx – 2ky + k² = 0 and ...

A: As per the question we have to find the volume of revolution of the area bou

Q: Let T : R? → R² be the linear transformation that projects vectors onto the line y = -x and then rot...

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Q: d the answer quickly

A: Given, x -2 1 3 7 y 6 10 12 35  To find Pn(x) : x=0        

Q: Consider the series In(k) k2 a) Enter an integral whose convergence or divergence is equivalent to t...

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: {{::) eR}. sider V = : #1, 22, 23 > 0 and ¤1, x2, x3 ER pose the vector addition and scalar multipli...

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Q: Find the solution of the initial value problem y"+ 4y+ 13y =0, y) = 0, y ) = 6. %3D y(t) = How does ...

A: Given y'' + 4y' + 13y = 0

Q: Find the volume of the solid generated of the area bounded by y = x², y + 2x = 8 and y = 0, rotated ...

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Q: A contract has been signed to leave a building at P200,000 per year with an annual increase of P1,50...

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Q: Given the series: 3 k k=1 does this series converge or diverge? O converges diverges If the series c...

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Q: 27 1+1 Evaluate the expression (2i – 1)² Express the answer in rectangular form. 1+i,

A: The rectangular form of a complex number is z=x+iy. The conjugate of the complex number: z=x+iy is z...

Q: dy et-y dx 2.

A: The given problem is to solve the given differential equation using separation of variables method.

Q: For the homogeneous Fredholm equation y(*)=2] sin(x+5) the'eigenvalue a and the corresponding eigen ...

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Q: 10 x2+9 dx 5

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Q: 5 Find: a f cos r dr Hint: In b sin r sin r sinr (1- cos? r)2 sin r, etc. b S sin r dr c sin r cos3 ...

A: 5a We have to evaluate the integral ∫cos3xdx. Rewrite the integral by using identities ∫cos3xdx=∫cos...

Q: What Mclaurin Series this function represents: (-1)"x?n (2n)! 1 - + - 2! 4! 6! a. e^x O b. cosx C. s...

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Q: 16 8 Find the value of x. SU (2x+21) 54° (5x+61 10 Find the length of KNJ. 48 J M

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Q: Express the given complex number in rectangular form (a + ib). 1. cos + i sin cOs + i sin

A: Since you have posted a multiple  question according to guildlines I will solve first   question fo...

Q: x-1)" log n Consider the power series where log n is the logarithm of n to the base 10. n=2 (a) Show...

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Q: Evaluate the moment Mx and My of the region bounded by y = 2x + 1, x + y =7 and x = 8.

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Q: a. 55.6209 b. o.007035. C. 5010.0 d. 4056.070

A: This is the question from approximation.

Q: Is there a solution y = y(t) of the differential equation y" + e*y = 0 satisfying lim y(t) = 2021? J...

A: We have a differential equation ,  y'' + ety = 0 First we will find solution of differential equatio...

Q: 4 Given the integral: J, 1+x? dx. Evaluate using Romberg's method. Tolerance = Nx10-6

A: As per the question we have to solve the given definite integral using the Romberg's method. With an...

Q: 11. Every line in R" is a subspace of R". 12. Every line through the origin in R" is a subspace of R...

A: This is a problem of linear transformation.

Q: 1-18i C. Find the complex numbers z that satisfy the equation 4z – 3z = 2-i

A: We have to find complex number Z

Q: Find the particular solution of y' - 2y = e3x if y(0) = -5 using Laplace Transform. %3D %3D

A: The given initial value problem is                                               y'-2y=e3x , y(0)=-5...

Q: ОЗх^2+2

A: x3-0.03x2+2.4×10-6=0

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: 2 Integrate the function f(2) = (z - 10i) from z = 0 to z = 5 + 5i along the line x = y.

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Q: x? + ах — 2bx — 2аb - х3 - 2ах? - 2bx? dx х* + ах3 — 2bxз — 2abx?

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Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear combina...

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Q: 2. Find the distance between the pairs of points using the distance formula. b. (4,8), (8,0) c. (0,5...

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Q: dy 2. х 3y : = x2 dx

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