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

Q: Show how to use the Intermediate Value Theorem to show that the equation z – V4z = 7 has a solution ...

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Q: Find the linearization at x = a. y = (10 + x)-12, a = 9 (Use symbolic notation and fractions where n...

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Q: Given that f(x) = x² g(x) = x + 15, find 11x and | (a) ƒ + g = (b) ƒ – g= (c) fg = (d)

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Q: Find the area under the curve y=x3+3x2 and the x-axis between x=1 and x3D3. O 46 sq. units O 54 sq. ...

A: We need to find the area under the curve y=x3+3x2 on interval 1, 3.

Q: logbx = .36 logbz = .83

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Q: Match the solution curve with one of the differential equations. O y" + 4y = 0 O y" + 2y' + y = 0 O ...

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Q: Consider the following matrices 1 1 -2 [ 1 | A В - 4 -3 1 -3 1 4 -3 1 2 -3 2 -3 4 Determins which of...

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Q: At what point does the graph of 3x+y=0 and x-y=D4 intersect?

A: Given: 3x+y = 0 y = -3x And x-y = 4 y = x-4

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Q: Consider the function f(x) given by the graph below. y f(x)

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Q: Assume that p, q : S' > → R are continuous and p + 0. Find all solutions of the differential S1 equa...

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Q: Find the general solution of y' = y sec x

A: Given, The differential equation y'=ysecx We have to find the general solution.  

Q: Ay Given y = x²+ 3x + 5, find Ax %3D Ay 2Ax + x + 3 Ay 2xΔx +x+3 Ax Ax O Option 1 O Option 4 Ду Ay 2...

A: topic - difference quotient

Q: f(x) = 8Vx + 1; g(x) = x² + 9 %3D

A: Given: - The functions are, f(x)=8x+1 and g(x)=x2+9 To find: - The value of f∘g and g∘f

Q: Evaluate the integral curves for the vector field F(x, y) =i -i .

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Q: Use the Chain Rule to evaluate the partial derivatives and dv ди se se at (и, v) %3D (-3, -3). f(x, ...

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Q: Find the equation for the plane through the points Pol- 1,5,- 3), Qo(-5,4.2), and Ro(3, -5,0). Using...

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Q: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

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Q: + 1)!. approaching the vertices of an equilateral triangle, each circle denominators? Use the patter...

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Q: Let f be the function below. You may click on the graph to make it lan Use interval notation to indi...

A: Given the graph is

Q: Find the derivative of the function f(x), below. It may be to your advantage to simplify first. f(x)...

A: The detailed solution is given below Thank you 

Q: II. Given the graph below, determine if the function H(z) is continuous at the following values of z...

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Q: Q2/ Find the distance between the point of intersection of the lines A & B and the point (4,-2), the...

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Q: Evaluate the definite integral: 4 dz

A: Evaluating the definite integral

Q: Consider the following. if x <1 if x 21' f(x) = a = 1 (a) Find the left-hand and right-hand limits a...

A: Topic:- calculus

Q: Let F(x) = f(r°) and G(r) = (f(x))° . You also know that a = 12, f(a) = 2, ƒ'(a) = 15, f'(aº) = 5 Th...

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x   Given: Fx=fx9 ; Gx=fx9a8=12...

Q: According to Newton's law of cooling/warming, the rate at which the temperature of a body changes is...

A: Find your answer below 

Q: 3x+4 > [1] S dx x² +3x+2

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Q: Consider the differential equation x²y" – 8xy' + 20y = 0; x4, x5, (o, ∞). Verify that the given func...

A: We have to find general solution Y.

Q: what is the avorago valus OF a Funckon F on an Posterval [a,b]? 13 the given by vallis of Fa)-tan X,...

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Q: E F Which blue function is the graph of the SLOPES of the red function? F

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Q: Prove that lim x² cos(1/x²) = 0. x→0

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Q: Use the figure to find the exact value of the trigonometric function. Find sin 20. 24 25 25 25 25 Qu...

A: As we know from the trigonometric ratios: sinθ=PerpendicularHypotenusecosθ=BaseHypotenusetanθ=Perpen...

Q: Evaluate the definite integral da

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Q: Consider the function f(x) = Complete the table below and sketch its graph. x 2 |-1 |-0.5 -0.1 F(x) ...

A: Given Data: fx=x+1x2+x

Q: Suppose that your best friend has calculated the partial derivatives of a given functionf(x,y)and to...

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Q: Calculate and at the points (7,41, 1) and (7, 41, – 1), where z is defined implicity by the equation...

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Q: The population, y(t) (in thousands) of rabbits on an island has an intrinsic growth rate of 28% per ...

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Q: y = x^2 + 2 and y =sin(x

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Q: Helpp

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled...

A: Given that: D(t)=4sin πt4+9π4+3

Q: 3. Find the general solutions rounded to two decimal places for each of the following. For each ques...

A: Given :a) sin 3x= 0.72sin 3x = 12The General solution is x=(8n-7)π2∪(8n-5)π2  ∀n∈ℤ  

Q: Find the partial sum S, for a geometric series such that a4 = 48, ag 1536, and n = :9. Sum =

A: Given that: a4=48a9=1536n=9

Q: Problem: 5 coordinates are given: A(-1, 4, 5), B(2, -1, -2), C(-6, -8, 3) in RCS; D(5, n, -12) in CC...

A: Given coordinates: In Rectangular Coordinate SystemA=-1,4,5B=2,-1,-2C=-6,-8,3In Cylindrical Coordina...

Q: cos? cos n 48. n2 n=1 IM:

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Q: Write the equation of the line tangent to the graph of the function at the indicated point. As a che...

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Q: P1. For each of the following infinite series: a) Determine n-th partial sum Sn b) Show whether the ...

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Q: Evaluate the definite integral: dz 15

A: We have to solve the given definite integral

Q: Given f(x)=−2x^2+4x+13, find f′(−4) using the definition of a derivative.

A: f'(a) = limh→0 f(a+h)-f(a)h.

Q: Jon's bathtub is rectangular and its base is 12 ft. How fast is the water level rising if Jon is fil...

A: Find your answer below