1. The sum of two positive number is 42. What are these numbers if their product is a maximum?

Q: Find the derivative of the function. h(s) = -2/75² + 9 h'(s) =

A: Given that hs=-27s2+9To find : derivative ,h'sSolution ;hs=-27s2+9h's=-2×127s2+9×14s

Q: raluate the integral / V4x4 – 12r2 +7 xdx. A - (4x* – 12r? +7)½ + c 24 B - {(2r²– 3) /4x+– 12x²+7 – ...

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Q: Car 1 is heading due south from Math-town at a rate of 40 miles per hour. Car 2 is heading due west ...

A: topic - application of derivatives

Q: Q5) A) Graph the curve Y = - 2 x (x - 4)(x + 6)(x - 2) between the value of x ( then find the area o...

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Q: dX; = X;(ydX, + tdt), d Хо 3D 1.

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Q: Question For j(x) = (-3x² - 8) (-6x + 9x), find j'(x) by applying the product rule. %3D Provide your...

A: The detailed solution is given below Thank you 

Q: Which of the following sets are equal? A = {x e R|-2sxs2} B = {x e Z|-2sx< 2} C= {x e Z*|-2 < xS 2} ...

A: So set C and D are equal. 

Q: dx (c) x² /4 – x2

A: Please see the below picture for detailed solution. 

Q: Use the formula for the sum of a geometric series to find the sum. (Use symbolic notation and fracti...

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Q: (2x2 + dx. Using u-substitution and transformation of integrand, then the power formula applies; suc...

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Q: Which of the following statements is true? The sequence {ln(n)}, is bounded, monotonic and converges...

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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: d²y and evaluate at (1, - 1): .2 Find X = t + 1 y = t2 – 1

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Q: II. Find the derivative of the following functions. 1. f(x) = x3+x x4-x2+1

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Q: Calculate the work done by the force F(x, y) = x3yi+ (x - y)j along the parabola y= x2 from (-2, 4) ...

A: To find the workdone

Q: Test the continuity of the function f(x): 3 – x X +1 2< x <3 3 < X < 4 X = 4 F(x) = 2х — 1

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Q: Renirite ecc of the fo1lawing buuting ఆUng (A10garithm oto singu algebraic quantity) - Inca) -'/3 In...

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Q: Using u-substitution, the integral Jf(x)dx reduces to a new integral J glu) du. If g(u) = u+1 , eval...

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Q: 6 - x 12. Solve the rational inequality x < 2x -5

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Q: 1 :dx J xV16ln² x – 9

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

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Q: II. find an explicit solution of the given initial value problem using separation of variables. 5. x...

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Q: Problem 1: Answer each of the following questions. (a) Give the candidate general solution using the...

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Q: Find dy/dx by implicit differentiation. x²y + xy2 = 8x %3D

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Q: Express the given quantity in terms of sin x and cos x. Sin (2n – x)

A: The given quantity is  sin(2π-x)

Q: n (a) Express lim as a definite integral. i=1

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Q: Given the differential equations functions f(x) and g(x), and their derivatives in the table below, ...

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Q: naximum revenue, and 5. Determine the net change and the average rate of change for the function f(t...

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Q: 3xy Consider L- lim 3)-(0.0) a- Find the limits along the paths x=my. (Hint Find your answer in term...

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Q: Find the maximum or minimum value of the quadratic function g(x) = 2x + 6x + 3.

A: Given,           gx=2x2+6x+3To find : The maximum or minimum value of the quadratic function.

Q: (x-1)+3(x-1) +5dx

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Q: 5. The sum of the first 12 terms of an arithmetic series is 186, and the 20th term is 83. What is th...

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Q: L{f(t)g(t)} = L{f(t)}L{g(t)}, where both f and g are continuous and of exponential order. True False

A: We have to find the reason

Q: f (x) = x6 + 12x 2 at x = 1 %3D

A: Here,            f'(x)=x6+12x-52'        =x6' +12x-52'        =6x5-30x72        =-30+6x172x72 And at...

Q: 24. A particle moves along the curve y particle passes through the point (4, 1), its x-coordinate in...

A: We have to find how fast is the distance from the paryical to the origin changing at this instant in...

Q: Consider the following differential equation. (25 - y?)y' = x2 x2 Let f(x, y) Find the derivative of...

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Q: E(-1)" (~1)nn! n=1 en

A: Given series:-       To find:- Given series is convergent or not

Q: 4.(Straightforward) Make the differential equation below exact by find- ing an integrating factor u....

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Q: e 4x =dx Ve4x – e

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Q: Use the formula for the binomial series: m(m-1)..(m-k+1). k! m(m-1) (1+ x)" = 1 + mx + oDx? + ... + ...

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the s...

A: find volume rotationg about x-axis

Q: B) Find the third derivative of the function: Y = + VX3 %3D

A: We have to find third derivative

Q: = p 4. o pui

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Q: Complete the following statements. Let P- be the inverse function of P. Take x to be an output of th...

A: We will find the inverse function  

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Topic:- sequence and series

Q: Determine f(x) so that cos(in?x) f(x) dx = sin (In²x) + C (A) (B 2 In x In x 2 In x (D

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Q: Find Ay and f'(x)Ax. For y = f(x) = X = - 1.6, and Ax = 0.1

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Q: %3D h that x+3y =16. |=

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Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27....

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Q: The graph of the derivative f' of a function f is shown. y 4 y= f'(x) 4 6. (a) On what intervals is ...

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