Which of the following describes a function? 1. y=x² +1 x=y² +1 1 I only Oll only I and II Neither I nor II.

Q: Solve the following equations 2)3x+2 = 27 1) 2Ln(√x + 3) + 2Ln(√x-1)=Ln(6x-7) I 1 1

A: Let's solve both equation.

Q: Given f(x) = x² sec x, find f'(x). Ox² cos x + 2x sec x O x² secx tan x + sec(2x²) O 2x sec x tan x…

A: f'(x)=x2secx'         =x2'secx+secx' x2        =2xsecx+secxtanxx2

Q: A cylindrical tank is full of water. If the radius and height, respective of the tank are 1m and 3m.…

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Q: Q4) If the power series method was used to solve the following ODE. (x-0.5)y"-y' + (x² - 1) y=0, x=…

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Q: dx sin x tanx

A: Here we have to solve only part b

Q: Differentiate g(N) = rN g'(N)= with respect to N. Assume that K and r are positive constants.

A: We need to find g'(N).

Q: Which of these series, if either, diverges? ∞ - 1)k 1. II. Σ(-1)^ (77) K²+1 k=1 k k=1 A. I only B.…

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Q: As shown in the required readings or videos use a power series to find a general solution to Airy's…

A: Given : Airy Equation : y"+xy=0

Q: 15. Use the results of problems 12,13 and 14 and assume that the Maclaurin Series expansion for ex…

A: We have to prove the given equation of complex number

Q: Evaluate: S O (1+2√√)¹ 2 O (1+2√)¹ +C 8 O 2(1+2√x) + C O (1+2√)¹ - + C 4 (1+2√x)³ - dx +C

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Q: c) What is the loss the company incurs when it tries to maximize sales (that is, produce the maximum…

A: Find out the loss the company when it tries to maximize the sales.

Q: An object is moving with velocity (in ft/sec) v(t) = t² - 2t + 2. At t = 0, the object has a…

A: Topic = Integration

Q: Find the arclength of the curve y = 3x² + 5 on [0,3].

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Q: 1)y= (8+7x³) Find the derivative of the following functions 2)y = (x +5)®(2x + 3) 3)y=

A: We have to find the derivative of the given function

Q: Investigate if the integral is convergent or not. Justify your answer.

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Q: integral

A: We will find the solution m

Q: 2. The base of a solid is an ellipse whose major axus and minor axis are 12 cm and 8 cm long,…

A: We need to find volume.

Q: Given the complex numbers z = 2 + j3,zz = -1 - j2,andzg=4+j4 find; Im (高)x+x@zs)+Im(zz+z) (元)

A: solution

Q: For the function whose graph is shown below, at which value of x is the graph continuous and…

A: We know  Function differentiable if it is continuous through out its domain   At sharp/corner points…

Q: 1.1 Determine the following derivatives with respect to x 1.1.1 y = cos(sin(cos.x)) 1.1.2…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Consider the following initial-value problem. y ′ + 3y = e−3t,    y(0) = 5 Take the Laplace…

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Q: Integration of { 8t^7dt

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Q: y = In(x-2) ex+1

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Q: x5 + x² + 4x³ + 4x² + 4x + 4 dx (x² + 2)³

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Q: Which statement describes this graph? 3 15- -10- -5-

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Q: 6. How many solutions does this system have? b) 1 d)i 10x - 7y=10 4x + 5y = 12 a) 0 c) 12 Ho…

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Q: Consider the following. [u-5(6 - u³ +4²0) du Simplify the integrand by distributing u¯5 to each…

A: We know that integration power rule is given as - Integration of xn is xn+1/n+1 +C ; here C is…

Q: Show your step-by-step solution. Find all the relative extrema and saddle points, if any, of the…

A: To find out the relative extrema and saddle points.

Q: f(secx tan² x) dx

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Q: Q19) The general solution of 2x2y" + 3xy' - 15y = 0, is: a) y(x) = ₂x² + ₂x³ b) y(x) = C₁x + c₂x-3…

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Q: 2 S-2 2 S+2 Option 3 Option 2 O *The Laplace transform of the x(t) is 2e21 1 S - 1 s²+1 Option 1 O…

A: Let's do laplace transform of given function.

Q: Q1) L-1 s(s a) cosht -1 b) 1-cosht c) (cosh2t - 1) d) (1 - cosh2t)

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Q: Find dy dx In y = e sinx Ody dx dy dx O dy dx O dy da - = = 1 = ye" sin x ye" cos x 1- ye" cos x yey…

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Q: 3) (11x + 17) dx 2x² + 7x - 4 S

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Q: A transportation company sells 2000 bus tickets per day when the price is $10 per ticket. They…

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Q: Question 4 (a) Solve the following: [²4x¹dx (b) Explain with the aid of a sketch how this value can…

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Q: Find F(s). ℒ{t3e−4t}

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Q: Solve step by step in digital fe 6x - 1 a) lím x→ 1/ 2x - 6 b) lím X-00 x² - 9

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Q: a) e b) e-t Q24) The Integrating factor which make (3x2y + 2xy + y³)dx + (x² + y²)dy = 0 exact, 15.…

A: A detailed solution is given below.

Q: en the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q +4Q² − 2Q³…

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Q: Find dy dx In y = e sinx O dy dx O dy dx O dy dx O dy dx = yey sin x =yey cos x = 4 1- ye cos x yey…

A: We can find the answer as below.

Q: Find the derivative: y = ln (3x + 1) O y = O y = Oj = 2 y = = 2ln(3 + 1) (3x + 1) 6 (3x + 1) 3 (3æ +…

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Q: 4. The equation of a plane is [x, y, z)=[-1,-1,1]+s[1, 0, 1]+[0, 1, 2]. Find the - intercept of the…

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Q: Find the rate of change of the volume (V) of a sphere with respect to its radius (r) when r = 4. 4π…

A: You must have idea about basics of derivatives. The rate of anything is basically the derivative…

Q: Given the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q + 40²…

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Q: 1 Given f(x)=³-57² +24r, which of the critical number found in the previous number is f(c) a…

A: You must have an idea about to how to find relative maximum or minimum using critical points.

Q: 3 i(z³+1³) lim z→-i_z²+1

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Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: *y=(2x^2+6) find dy\dx 4x\(2x^2+6) O 6x O 4x\(2x^2+7) O

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Q: Differentiate the following expression: y = x² cos 4x

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