Use the Laws of logarithms to rewrite the expression 3 (212. √/y13 in a form with no logarithm of a product, quotient or power. loga (21¹2. √/y13) =

Q: 16. x²y" (x) + 5xy' (x) + 4y(x) = 0 ; y (1) = 3, y' (1) = 7 17. x³y"(x) + 6x²y"(x) +29xy' (x) -…

A: The given differential equation is;  x2y''(x) +5xy'(x) +4y(x)=0, y(1)=3, y'(1)=7.

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Q: Solve the differential equation by variation of parameters. y" + y = csc(x)

A: Our Aim is to solve the differential equation given below using variation of parameters.y"+y= csc…

Q: 3 5 58 a. A-¹BT Given A = and B = -2 -5 3 7 find

A: Solution is given below:

Q: By power Series method, Solve the following ODES • (2+x)y=y ans: y = a. (1+1=1/2 X

A: In this question we have to find the solution of the power series.

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Q: For what value of the constant c is the function ƒ continuous on (-∞, ∞)? cx² + 2x if x 2.

A: We know :- Limit definition at x=a  ⇒limx→a-f(x) =limx→a+f(x)  if function continous at x=a then…

Q: Find the Laplace Transform of f(t) = sin2tcost A B 2 54 +55² +4 2 Ⓒ 4 E s² +3 s+10s² +9. ( 5++55²+4)…

A: Given problem:- Find the Laplace Transform of f(t) = sin2tcost

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A: The given function is y=x2+13x-2x2

Q: нх У - 169 = 19.2 ё + воё, усо) =ўс) 4Х 4X -4Х Ans: y=2.2 +e+24xe X - Че

A: Solution of given question is written in below steps.

Q: 9-x2 x dx

A: ∫9-x2x2dx=∫cot2udu=∫ -1+csc2udu=-∫ 1du+∫csc2udu=-u-cotuSubstitute back…

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Q: f(x) =  5 x2 + 6 Describe the interval(s) on which the function is continuous. (Enter your answer…

A: Polynomial function are continuous every where so using this we solve this problem

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A: The initial amount P=$5000 Rate of interest r=4%=4100=0.04 p.a. The time period t = 5 years

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Q: Problem 2.11 For what values of x is f continuous? f(x) = { 0 if x is rational x if x is irrational.

A: We have to check the continuity of the function.  For continuity, left hand limit = right hand limit…

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Q: =4 Sin4n 3n A. The limit of the sequence is: B. The sequence diverges.

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A: Given equation, y=x+1x2+1

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Q: ƒx(2x−1) dx 2 √x³√x²+4 dx

A: for (1),     ∫ x2x-17dx=∫ 128x8-448x7+672x6-560x5+280x4-84x3+14x2-xdx=∫ 128x8dx-∫ 448x7dx+∫…

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Q: QUESTION 1 P 0 0 9 0 00r Show that 0 Hence, determine the inverse of the following matrices: 100 i.…

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Q: Given f(x) = x² + 7x + 6, find the following. (a) f(0) (b) f(1) (c) f(-1) (d) f(-3) (e) f(a) (f) f(x…

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Q: Suppose that the cost function for a product is given by C(x) = 0.003x³ +8x+11,440. Find the…

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Q: 1. [cos³x dx [Use the reduction formula]

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Q: 4 3 1 -1 & Find lim The graph of the function f(x) = tanx is given above for the interval z = [0,…

A: Topic = Functions

Q: 1. (Use a calculator) Write down the equation used to evaluate the following expressions, and then…

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Q: Problem 2.7 Let Find the limit lim f(x). x 0 f(x) = x² if x is rational 0 if x is irrational.

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Q: question#22

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Q: down oes... not a precise m However, with ann an algebra c concave do rate of chang creasing y…

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Q: 7. dx S- X-3√x²

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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Q: Consider the following planes. -6x + y + z = 6 24x - 4y + 6z = 36 (a) Find the angle between the two…

A: Given problem:- Consider the following planes. - 6x + y + z = 6 24x - 4y + 6z = 36   (a) Find the…

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Q: Consider the following differential equation to be solved by variation of p y" + y = csc (x) ind the…

A: The solution is given below

Q: (a) Find the derivative of ƒ (2) = (x² + 5) (8æ — 5) by first expanding the polynomials. Enter the…

A: We have to find out derivative

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Q: Solve 4 sin x = 1.35,3.65 x = 3 for the four smallest positive solutions Give your answers accurate…

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