Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) log3

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Q: Consider the following equations. y f(y) V 25 - g(y) = 0 y = 2 Sketch the region bounded by the…

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Q: 1. Answer the following questions for the quadratic function f (x)=x² -8x +8 . a. Calculate the…

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Q: 1. (1 + y?)° dy 2. S sin x+cotx dx sin?x

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Q: Let limf(x) = 3 and limg(x) =. Find

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Q: Find the general solution of the differential equation and check the result by differentiation. dy =…

A: The given differential equation,     dydt=16t7

Q: dy

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Q: 8. (x'-20) (x-3)

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Q: Consider the function f(t) = 6 sec (t) – 6t°. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: Use the integral test to determine whether the series converges. Σ 4n - 1 n=1 converges diverges

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f() = 2x + 3 between x =…

A: Our Aim is to find the "area under curve"of f(x)=2x+3 between x=11 and x=13using the Fundamental…

Q: A Comapny's Marginal cost function is C^1(x)=17/√x) Where X is the number of units. Find the total…

A: Use integration for finding the cost function.

Q: 3. 1 1 2 4 1 To find the blue shaded area above, we would calculate: | f(x)dx area а Where: a = b :…

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Q: Consider the two series: 6n (a) > 5n + 39 n=1 1 (b) n2 In n n=1 Which of the following statements is…

A: Use roots test for checking the convergence  of the series .

Q: D. Find The or mogonal traectory of the family f aurves y=

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Q: 8 tan¬1 n 1 + n² 00

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Q: Write the equation of the function graphed below.

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Q: Which identity is most useful in evaluating sin² x dx? sin? x + cos? x = 1 cos 2x x = 1- 2sin? O…

A: The given integral,         ∫sin2x dx

Q: Given the equation 2x + 3y = 6, a second equation that forms a system with no solution is: O 2x – 3y…

A: Given; 2x+3y=6

Q: Determine the area of the gtven reglon. y = x + sin x Step 1 Note that for the given reglon, x…

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Q: 9) Find the vectors angle between the twe

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Q: 5y² = 2x³ – 5y

A: Derivative with respect to x

Q: Evaluate the following algebraically. csc? x lim 1 O 1 O -1 8. 8.

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Q: 8. True or False: If lim an = 0, then an converges. %3D n=0 (a) True (b) False

A: Solved below

Q: Use the fourth Taylor polynomial for f(x) = Va at a = 9 to estimate v10. Round your answer to four…

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Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: A ball is shot from the ground straight up into the air with initial velocity of 43 ft/sec. Assuming…

A: To find the height  ball goes up to.

Q: 14. If a baby is dropped from a height of 300 meters, its height s at time t is given by s(t) =…

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Q: Find the distance from A to C across the gorge illustrated in the figure. 130 ft The distance from A…

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Q: Given t2 – 4 f(x) = dt 1+ cos2(t) At what value of x does the local max of f(x) occur?

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Q: QUESTION 3 Find a formula for the nth term of the sequence. 1, 4 9' 16 25 (reciprocals of squares…

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Q: c). Using an integrating factor solve the equation dy + 2y/x = x dx

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Q: Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 convergent or divergent. b)…

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Q: e sin. *(sin x + cos x) dx ecos x

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Q: Evaluate the definite integral by the limit definition. Step 1 To find the definite integral 9 dy by…

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Q: Find the general form of the equation of the plane containing the point Q(0, –2, 10) and the lin l1…

A: Let's find.

Q: Since the start of July, OHaganBooks.com has seen its weekly sales increase. OHaganBooks.com fits…

A: For (a), w'(t)=36t2+252t+6242' =72t+252 For (b), For t=1, w'(1)=72+252=324

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 3z F(x) = | cos (t°) dt.…

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Q: Consider a population of a certain country that is observed to grow exponentially. Based  from the…

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Q: Determine if the geometric series converges or diverges. If it converges, find its sum. 24 3 4 + 1+…

A: Given query is to find series converges or diverges.

Q: Find two positive numbers that satisfy the glven requirements. The second number Is the redlprocal…

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Q: (d) sec(x) – sec(x) sin²(x) = cos (x)

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Q: Consider the function f(x) = 8/a + 1 on the interval [4, 6]. Find the average or mean slope of the…

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Q: Three forces are simultaneously acting on an object. The first force is 1200 N downward, the second…

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Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: Given Rn 2 4 2 6( 6 + i- 2 3(6 + i- express n i=1 n n the limit as n → 0 as a definite integral,…

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Q: If f(x) = | ( + 2t² + 2)dt then = (x),,f

A: f(x)=∫0xt3+2t2+2dt

Q: dz dz and dy dx Suppose z is a function of x and y, and tan y² + x² = z®e6y. Solve for

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Q: 2x 3x Evaluate the given limit of lim + if it exists. I – 1 I +1

A: Follow the procedure given below.

Q: Condense the expression to the logarithm of a single quantity. 4 log (x) log4(y) - 3 log4(z)

A: Given query is to compress the logarithmic expression.