Find the equation of the line tangent to the graph of f(x)= (In x)2 at x= 3. y%3D (Type your answer in slope-intercept form. Do not round until the final answer. Then round to two decimal places as needed.)

Q: If the domain of the function f(x) is {r E R| – 2 < x < 4}, the the domain of the function g(x) = f(...

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Q: S*(1+v*) -\dv (cot-ly2) 2.

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Q: . Use the appropriate limit laws and theorems to determine the limit of the sequence. an=(3+8/n^4)^1...

A: We will evaluate all above as shown below

Q: A glacier in Republica was observed to advance (h)2.5______ inches in a (i)____71_______ minute peri...

A: This is a basic problem of calculus

Q: Determine the form of a particular solution of the differential equation y" + 9y = e*cos3x + x² + x³...

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Q: Evaluate f"(e) when e = 0 given f (e) = 2 sec 30

A: Given that: f(θ)=2sec3θ

Q: Suppose the cost of producing bananas is given by the differntial equation: dC/dx = 26/x + 45x whe...

A: The cost of producing bananas,dCdx=26x+45x

Q: Question The graph of the polynomial f(x) is given below. If f(x) has degree 4, find the factored eq...

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Q: (In(x))? 3

A: We have to apply rules of integration to solve the problem

Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +...

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Q: "J-Hope" PROBLEM SOLVING A bacterial population Z is known to have a rate of growth proportional to ...

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Q: Find the slope of the line tangent to the curve x + sin(y+π) = 2x3 + ey at the point (-1,0). Show wo...

A: Topic:- application of derivatives

Q: II. Let U = R, 1 = { x eR | x5 – 26x3 + 25x = 0 }, J = { x € R | |4x + 2| > 10 } and K = { x €R | x?...

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Q: write the given expression in the form of u^2 - a^2: x^2 - 6x + 5 is equal to. SUBMIT YOUR SOLUTION ...

A: Here we have to use the completing square method

Q: 3. For the given function below, find 2x* - 3x3 - 21x? — 2х+ 24 y : 2x* -7x3 —11х? +22х +24 E. Infin...

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Q: If the solution of y' = 2(2x - y) passes through the point (0,1), determine x when y = 7.

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Q: find the average value of the function on the given interval 7T 5. COS on 0, 6. sin x on (0, 7)

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Q: Which of the following is not in the domain of tan(x)? Select all correct answers.

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Q: 49x2 – 75x 19- 4x - lim X -00 86x +7

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Q: Let ä = = (8,1, –4) and b = (5,-2,1). Find à + b, 4à + 2b, là\, and là – b\ %3D

A: a vector = &lt;8,1,-4) and b = &lt;5,-2,1&gt;  Find , a+b, 4a+b, |a| , |a-b|

Q: Scscx cotx sin (csc x )dx

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Q: 10 dS (3t2-12t-15)dt %3D

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Q: Find the limit of the infinite sequence. (2n–1)² n²+8 tn Enter dne if the limit does not exist. If t...

A: Given that: tn=(2n-1)2n2+8

Q: QUESTION 1 d²y Find dx² for each of the following equations. a) y = 3x² + cos(3x) b) y = e** + (x + ...

A: Given that: (a)y=3x2+cos(3x)(b)y=e4x+(x+1)4

Q: 1. fcos*ysin ydy

A:  In this integral,  you can see cosy2 has exponent 4 and siny2 has exponent 1. To solve this integra...

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

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Q: Write the function g(x) (in blue) in terms of the function f(x) (in red). 2 -3 -2 6. -1 5.

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Q: (4x^4+x^3(y)+y^4)dx+x^4dy=0, Solve for HOMOGENOUS DE

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Q: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

Q: 2メー7 f xス」

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Q: A rectangular storage container with an open top is to have a volume of 10 m³ . The length of the ba...

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Q: Median Home Prices The median home price in a certain country over the period January 2010-January 2...

A: Given:- Median Home Prices The median home price in a certain country over the period January 2010-J...

Q: Write out (but do not compute) 5 other iterated integrals that are cquivalent IT [ f(r,y, 2)dz dz dy...

A: Given:     Limit: ( 0-4 , 0 - y2 , 0 - y )  f(x,y,z) dx dz dy  

Q: kf (x) dx =k ] f(x)dx Jas(a))dx=f (x) +C D

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Q: 17. An open top box has the dimensions as follows: height: x width: (13-2x) length: (17-2x) a.) Writ...

A: Given: height= x width= 13-2x length = 17-2x  

Q: If a sequence c1, c2, C3, . .. has limit K then the sequence eº, e%, e,... has limit eK. Use this fa...

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Q: x(x* –1) dx x' +1

A: This integral is of expression a2 + x2 . 

Q: Question Evaluate the following limit using L'Hospital's rule. lim (e + 2a)() 6x Provide your answer...

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Q: 28. tan (2x) sec (2x) dx

A: follow the procedure given below.

Q: The distance of a car from the drivers home after x nours is given by the expression D (x) 2x2 + 20 ...

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

Q: Variable Separable (8) dx dy e 3x+2y; Provide the explicit solution (9) secx dy = sec 2ydx

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Q: Consider the function f(x) = -6x2 + 4x – 6. (a) Find all critical numbers c of f. c= (b) The local m...

A: topic - application of derivatives

Q: Pescribe how the graph of the function g(x) = - x can be obtained from the basic graph. Then graph t...

A: f(x) = xmultiply  by 1414f(x) =14 x      ( Vertical Shrink by 14)now multiply by (-) sign -14f(x) =-...

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. ...

A: Our Aim is to determine whether the given sequence limn→∞ -8n!nn-(i)is convergent or divergent.

Q: 1- Solve the following equations using Grammar's rule: b) 2x + y - z = 2 x - y +z = 7 2x + 2y + z = ...

A: Given system of equation2x+y-z=2x-y+z=72x+2y+z=4We know that for system of equation a1x+b1y+c1z=d1a2...

Q: 4

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Q: Find the derivative of a function f(x)=(x^2+1)^3 (2x−1)^4 f ' (1) = ____

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Q: 1. Prove that lim (10z – 7) = 3 using epsilon-delta definition of a limit.

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Q: Question Suppose that the following functions all have the given limit at a = -1. lim f(x) = 0 lim g...

A: Given that:                  

Q: Students in a zoology class took a final exam. They took equivalent forms of the exam at monthly int...

A: Given:The average score in percentage is given by: