In x to show that In a loga x = Use the change of base formula loga x = x In a loga x dx dx In a In x dx 1 In a

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A: Given query is to solve the differential equation.

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Q: There is a removable discontinuity at x = 1 and f(1) = 4

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Q: Find y' and y". y = e4e* y' = y" =

A: Explained below 

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Q: = Homework: HW11--3.2 a. Find the derivative function f' for the function f. b. Find an equation of ...

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A: We will use the concept of compound interest to solve this.

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Q: 3.) dx + e dy = 0

A: The objective is to find the solution of the differential equation.

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Q: Problem B.7 Express each of the following ODES in the standard form y" + P(x)y' + Q(x)y = f(x). Do n...

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A: Since multiple subparts are asked, I am answering the first 3 subparts only.

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A: The direction plot is:

Q: Find the amplitude of the graph of y = - 5 sin O 167 8. 05

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Q: 3. lim f(x) = -2, X-2 4. X-3 lim f(x) = +00, lim f(x) = 2 and f(2) = 0 lim f(x) X-3* %3D = -00

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Q: In the answer box below, type an exact answer only (i.e. no decímals). You do not need to fully simp...

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A: NOTE: Refresh your page if you can't see any equations. . take derivative

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Q: Evaluate the following improper integrals to determine if they converge or diverge. integral converg...

A: Note: As per our company guidelines we are supposed to answer the three sub-parts of the question. K...

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A: Simpsons rule

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Q: QUESTION 2 of where f(x.y)- sin ду Oa. X Find O b. -X cos O. y-X cos O d. 1 O e. None of the other c...

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Q: 3. Let f(x) = 2 sin(3x) + 4 for x E R. a. The range of f is k s f (x) こらし2sim6xド2-0sn 6x)10100rnbとる ...

A: Given:-  Let f(x)=2 sin(3x)+4  And g(x) =5f(2x) d. Find the period of g. e. The equation g(x) = 12 h...

Q: - Show that lim sin a =D0.

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A: topic - functions

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Q: If e = 3 10x find the reference angle 0'. Give only exact answers, and type pi for a if needed. Do N...

A: Topic = Trigonometry

Q: find d^2/dx^2(sinx+cosx)

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Q: dx 3x2 + 11x + 6

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Q: Let f(r) be the function 6r2 /(5+h)-f(5) 5x +9 Then the quotient can be simplified to ah + b for and...

A: Given query is to find the value of a and b.

Q: exV – 1 Let g(x,y) (a, b) = (1,0). Show that lim g(x,y) does not exist. (x,V) - (a,b) %3D %3D x+y - ...

A: Firstly it should be proved that limit does not exists and then recognize the two limit values so th...

Q: Question 1 Consider the function (x²y² – y³ x² + y2 0, if (x, y) # (0,0) f(x, y) = if (x, y) = (0,0)...

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Q: Use the difference an+1 - an to show that the sequence {n – 11"} +00 | is strictly increasing or str...

A: see below the answer and calculation

Q: 3. v? – 4v = -1.2975 – 2.1i

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. ...

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Q: The projected population of a certain ethnic group(in millions) can be approximated by p(t) = 38.96(...

A: 1. p(t)=38.961.017t, where t=0 corresponds to 2000 Note:    multiple questions are given we are answ...