Problem 4 Show that arcsinh(x) = sinh(x) = In (x+ V/x² +1). %3D int: Let y = sinh¬' (x). Then x = Ive for y. sinh (y). Now, use the definition of the hyperbolic sine to

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Se...

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Q: A model for tumor growth is given by the Gompertz equation = a (In b – In V) V where a and b are pos...

A: Given:  A model for tumor growth is given by the Gompertz equation, dVdt=aln b-ln VV, where a and b ...

Q: Given that f(−5)=−10 and f′(−5)=−2, find an equation for the tangent line to the graph of y=f(x)at x...

A: Topic = Functions

Q: -8 dx J3 (x2-12)

A: Here we have to solve the given integral.

Q: Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of...

A: The given function is: f(x,y)=y+sinxyGiven point is:  P=(0, 3)

Q: b) E(-1)"+1 Vñ Inn n-1

A: The given series is: ∑n=1∞nln n which is an alternating series with bn=(-1)n+1nln n, n≥1  

Q: Find the equations of the tangent and normal line to the following curve at an indicated points

A: Given that: y=31+x

Q: 4t2+3t sin t 2. lim t 0 t2

A:

Q: sec" y dy- (f) tan y

A: Topic = Integration

Q: -dx. Evaluate ſ &-3)(x*-1) ,. х2-2х-3

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Q: Find equations of the tangent plane and normal line to the surface z + 19 = xe cos z at the point (1...

A: We have to find tangent plane equation and normal line.

Q: x+tan x 4. lim X→0 sin x

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Q: The acceleration of a moving particle at any time t is given by expression 6t – 24. Find the positio...

A: given acceleration a(t)=6t-24  

Q: (a) What is the rate of change of f(æ, y) = 2xy + y² at the point (2, 1) in the direction i = –3i – ...

A:

Q: Find the slant asymptote with limits

A: Given function f(x)=(x-2)(x+2)(x+1)(x+3)(x+1)

Q: Evaluate and state limit laws used

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Q: Suppose that lim (x,y)→(3,1) f(x,y) = 6. What can you say about the value of f (3,1)? What if f is c...

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

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Q: A parallelogram is formed by the vectors [1, 2] and [3, -4]. Find the area of the parallelogram. O 1...

A: Given query is to find the area of parallelogram.

Q: It is possible for la + b| < ]ã|

A: topic- vetors

Q: Find lim (x,y,z)-(0,0,0) x²+y2+z4 xy+yz?+xz2 if it exists, or show that the limit does not exist.

A:

Q: A trough is 16 ft long and its ends have the shape of isosceles triangles that are 3 ft across at th...

A: A trough is 16 ft long and its ends have the shape of isosceles triangles that are 3 ft across at th...

Q: (b) y = e-u cos(u) dy = -e"sin(u) – e"cos( u) os u

A: The given function,  y=e-u cos(u)

Q: The temperature at a point (x,y,z)(x,y,z) is given by T(x,y,z)= 1200e^(−x^(2) − 2y^(2) - z^(2)) whe...

A:

Q: k-1 Since the series can be rewritten in the form it is a geometric series with: k=1 a = r = Give ex...

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Q: The set of complex number, write in roster method (at least 10 elements) and set builder notation

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Q: dy (8y – a²y) + x – xy² = 0 dx

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Q: 1. Find an equation of the line that is tangent to the graph of f and parallel to the given line. 1 ...

A: Topic = Functions

Q: lā + b| = |a + b|

A:

Q: degree

A: We will find the equation. 

Q: Determine if the series converges or diverges. If the series converges give its value. 10 Σ 00 n=4 п...

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Q: Let f(x) = and calculate x(In(x)) f(x) dx by using integration by substitution. What was your substi...

A: Given that: f(x)=1x(lnx)6

Q: ex sin(e*) dx cos?(e*) [sec2(e*)+18]

A: The solution is given in the next step.

Q: Determine whether each integral is convergent or divergent. Evaluate those that are converg 1 9. d.x...

A: If limit of improper integral is given and is finite, Then it will converge.

Q: proj„b is always less than |5 1|

A: We will use the definition of projection vector and will use the Cauchy-Schwarz inequality.

Q: For the function y - f(x)- 2x + 0: df at = d.x a. Find 4. f'(-4) = 96 b. Find a formula for a 1 df a...

A: Answer: a.) ddf(2x3+0) = 6x2 =f'(x)f'(-4) = 6×(-4)2 = 96   b.) y = f(x) = y = f(x) = 2x3 + 0y = 2x3 ...

Q: tan x sec xdx

A: Follow the procedure given below.

Q: Determine whether the integral is convergent or divergent. The integral from -2 to 14, 7/(x+2)^1/4 d...

A: integration ∫-2147x+214dx

Q: 21. 22. (D' + D - 9D' – 13D² + 8D + 12)y 0. Ans. y Ce+cze

A: We will solve the given differential equation.Below find the solution in the image.

Q: Multiplicities Use the images to determine the multiplicity (or power) for each root: (-1, 0) (0, 0)...

A: Given query is to find the multiplicity of each root of the polynomial from the graph.

Q: Find the equation of the plane that contains the point (3, 2, 3) and the line  x = -4 +4t, y = -3t,...

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Q: How much money must you invest now at 4.5% interest compounded continuously in order to have $10,000...

A: We know continuous compounding formulaP(t)=P0ert where value at time t P0=principal amount r= annual...

Q: 5. f(x) = In(x + 5) – 2 Domain: Range: Equation of Asymptote: End Behavior: lim f(x)= x→-5* lim f(x)...

A: Given : f(x) = ln(x+5) -2 To find : Domain, Range, Equation of Asymptote, and End behavior. 

Q: A country's production of solar power, in megawatts, can be modeled by f(1) = 440(1.4) , where t is ...

A: This question is related to differentiation, We will solve it using given information. 

Q: (х — 2)(х + 2)(г+ 1) (г + 3)(ӕ + 1)

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Q: zeros of the function f(x) = 12x - 19x2 - 101x - 60. Enten ced by commas.

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Q: 2. Use the following information to write out the polynomial functions in factored form. Sketch a gr...

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Q: an be sold at a price of Sp. For x-p"-7p+600, find the rate of change of p with respect t ...

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Q: Use implicit differentiation to find y' for the equation below and then evaluate y' at the indicated...

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Q: b) Suppose that f(x) 1 if x is negative. Can ƒ be continuous at x = 0?

A: