Consider the function H(x)= (e^3x)/(x^3) a. Find the derivative of the function b. Find the equation of the tangent line when x=1

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Q: √2, and 4. Let a₁ = V an+1 = √2+ an Vn E N. Show that {an} is a monotone sequence by mathematical…

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Q: Rewrite logg (13) as an expression that only has terms involving log10-

A: Concept: Change of base rule of logarithm logb(a)=  logx(b)logx(a)

Q: x + 1 x-1 1. Given: f(x) a.) solve: (fog)(0) = and g(x) = x-3 x + 3 b.) Find the domain of f,domain…

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Q: Evaluate the limit, if it exists. 1 - 2x² - x4 5+x - 3x4 1 2 (i) lim x → ∞

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: A particle moves along a horizontal line so that its position s at time t> 0 is given by: s (t) =…

A: Given query is to find the velocity of the object.

Q: Let f be a function that is continuous on [1,7] and differentiable on (1,7). Suppose 2 < f'(x) < 3…

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Q: Determine the type of DE (select all that applies): dr dᎾ + rsec0 = cos( Separable Exact None of…

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Q: A Moving to the next question prevents changes to this answer. Question 1 Given: y² + t2 + (e²y +…

A: The given equation is; y2+t2+(e2y+2ty)y'=0, y(1)=0.

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 O A.…

A: solution of differential equation

Q: 3. xcsc()-y|dx + xdy = 0

A: Concept: Any equation with one or more terms and one or more employee derivatives of the dependent…

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Q: Find the limit. lim (1)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: QuestivII Determine which of the following tests would be best to use to determine the convergence…

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Q: If f(x) = 7 sin x + 10 cos x, then f'(x) = f'(3) = (round to 3 decimal places)

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Q: Find the rate of change of a population of size P(t) = ³ + 4r + 10 at time! = 4. The rate of change…

A: P(t)=t^3+4t+10         rate of change=dP(t)dt             dt^ndt=nt^n-1

Q: Given: y2 + t2 + (e2y + 2ty)y' = 0, and y(1) = 0, Find: C (constant) O A. 1 OB. 0 O c. 1/2 OD. 1/4…

A: Given y2+t2+e2y+2tyy'=0 and y1=0

Q: Given 4x - -3x-y-7√ √/5y+ 8z = 5, calculate Provide your answer below: dz dx

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Q: In each of Problems a. Determine 16 through 1. a suitable for for Y(1) if the method of undetermined…

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Q: Given that lim f(x) = -6, lim g(x) = -9, lim h(x) = 7, find the following limits 24+00 8418 2448…

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Q: Differentiate the given function using the appropriate rule(s). Your answer does not have to be…

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Q: Find the equation of the plane that is tangent to the sphere X² + y² + Z² 14 at the point (1, 2, 3).…

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Q: Evaluate the integral. (Use C for the constant of integration.) √(x² + 8x) cos(x) dx (x²sin(x) + 8x…

A: NOTE: Refresh your page if you can't see any equations. . use the integration-by-parts method…

Q: Exercise 8 Form the difference quotient lim h→0 Exercise 9 f(x+h)-f(x) h Evaluate the limit lim (x².…

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Q: Determine the type of DE (select all that applies): 2xy dx + (y² + x²) dy=0 Linear Exact Separable…

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Q: Solve the equation using the quadratic formula   6x squared + 10x +2 = 0

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Q: Differentiate the following function 3 U = ²³² √² + ² + 2 u= +2√+³

A: Derivate with respect to t

Q: Given that; f(2)=2, f'(2)=3 g(2)=6, g'(2)=4 Calculate the following (fg)/2= (f/g)'(2)= (g/f)'(2)=

A: Please see the below picture for detailed solution.

Q: The function f(x)= x³ + x-1 has a root between 0.6 and 0.8. It is: Enter your answer with at least…

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Q: ow If w = −6x + 2yª, x = 3s +7t, and y = −8s — 6t, find Ət Sorry, that's incorrect. Try again? Əw Ət…

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

Q: If f(x)=6+(6/x)+(6/x^2)  find f'(x)

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Q: 29. Parametrize the part of the intersection of the surfaces y²-2² = x - 2, y² + z² = 9 where z≥ 0…

A: Given equations:- y2-z2=x-2 y2+z2=9

Q: Find f'(9) if f(x) = 7x² +6x + 2 √x f'(9)=

A: we know, ddx(xn)=nx(n-1) for any real n

Q: What values of a and b make the function f continuous everywhere? x² - 4 a = f(x) = " X 2 ax² - bx -…

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Q: Given: y' + y = y²(cosx - sinx)and y(0) = 2, Find C OA0 OB. 1/4 O c. 1/2 OD. 3/4 ⒸE. None

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Q: A tank with a capacity of 400 L is full of a mixture of water and chlorine with a concentration of…

A: Given A tank capacity is  400L , chlorine with a concentration of  0.05g/L Fresh water enters at…

Q: The area of the region inside r= 2 + sin and outside r= 2-2 cos 0 is given by

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Q: Consider the function f(x)=x³-2-x+2 that has exactly one root. Which of the following intervals…

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Q: Question 2 What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y'…

A: To find the general solution of the given equation. cosx+y+2x+cosx+y+4yy'=0

Q: 2. Express as a power with base 3. a) 9×3* b) 2x c) 9¹ d) 27**2

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Q: Question Determine the sum of the convergent series below. Leave your answer as a fraction in terms…

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Q: Given the scatter plot shown, determine if the correlation is positive, negative, or if there is no…

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Q: Use the Bisection Method to approximate, accurate to two decimal places, the value of the root of…

A: Use the Bisection Method to approximate, accurate to two decimal places, the value of the root of…

Q: ouncements dules cussions des norlock Find the equation of the tangent line to the given function at…

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Q: 4. For each differential equation and function x₁(t) given in parts (a)-(c), x₁(t) is a solution to…

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Q: Conic, your favorite math themed fast food dri- in offers 26 flavors which can be added to your…

A: Given that there are 26 flavors. 5 flavors to be added in the soda any of the flavors not use more…

Q: S S cos(x)√9+ cos²(x) arcsin (y)

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Q: dy Find Do not simplify. dx (a) cos (x + √y) + tanh ¹(sin²x) = ln 3 + y sech - x²

A: we need to find out the dy/dx.

Q: Find a vector function that represents the curve of intersection of the elliptic cylinder given by…

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Q: Leta = (5₁5) and b=<3₁-5) SO Why that Ba Sa+t6=<-4₁-207 S= +=D]]

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