Let f(x) = x for x < 0 and f(x) = sin(x) for x ≥ 0. Match the following. Here DNE means does not exist. ƒ" (0) ƒ'(0) f"" (0) Choose... + Choose... Choose...

Q: Differentiate the function. g'(x) = g(x) = In(xe−8x)

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Q: Let f(x,y) = 5xy4 + 5x²y. Find 224 ах = a²fa²fa²f 1 2' ахду' ax2' ay²' and 224 дудх

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Q: If A and B are constants, find where f''(x) = 0 I= f(x) = 9 Ar² + 7. Bx³

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Question 1: Find an explicit formula for the geometric sequence with a₁ = 10 and a4 = 80. a_n=…

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Q: 5) Find the divergence of (√x² + y² + z 5) ki vj + zk)

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Q: For a given commodity and pure competition, the number of units produced and the price per unit are…

A: Let's find consumer surplus and producer surplus.

Q: (a) Find the velocity v (t) - |a| (b) Find the acceleration function. 71 sin (a) e7 [7 sin(81) + 8…

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Q: Find the derivative of the function. y' = an−¹(x - √√₁+x²) 2 1 y = 5 tan

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Q: Differentiate. g'(0) = g(0) = eº (tan(0) — 0)

A: dexdx=ex  d(tanx)dx=sec2xd dx(a.b)=adbdx+bdadxgiven  g(θ)=eθ(tanθ-θ)

Q: Suppose that an automobile's velocity starting from rest is v(t) = lecimal place. O 3.3 ft/sec2 O…

A: Acceleration

Q: If a loading ramp is placed next to a truck, at a height of 8 feet, and the inclined portion of the…

A: Given query is to find indicated angle.

Q: Integrate using u-substitution or 2 guys in Jail. fx sin(2x²) dx 5. (4x³-2)7 (24x²)dx

A: (4)   I=∫xsin(2x2)dx∫sinxdx=-cosx+cdxndx=nxn-1

Q: Find the Binomial series for 1 (1+x)²

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Q: -t g(x) = f* e²²-¹ dt Sx

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Q: Match the following functions with the general shape of their graphs. Functions f(x) = ln (x + 2) -…

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Q: Find the area of the shaded region. Ay 121- 99- 77- 55- 33- 11- y=121-x² -33- -55- -77- -99- -121- X…

A: To find the area of the shaded region.

Q: ) If we would like to solve the following differential equation by variation of parameters 3x then…

A: We check whether the statement is correct or not .

Q: √2² This can be transformed into a basic integral by letting Consider the indefinite integral U= du-…

A: We have given an indefinite integral  ∫x5·x6-24 dx Let,  u=x6-2 du=6x5 dx So, integral will be…

Q: Find the Taylor series expansion of f(x) = = = at

A: we have to find taylor series expansion of f(x)  f(x)=1x2= x-2   at  a =1   now ,    f(x)=x-2…

Q: Graph the circle given below by moving the key points: To graph the circle, drag the center point to…

A: Solve the following

Q: 15. If g(x)=√t² - 5t dt, find g"(x).

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Q: Use logarithmic differentiation to find dy/dx. (x + 1)(x-2) (x - 1)(x + 2) dx || y = X > 2

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Q: Use the graph of f(x) shown below to answer the questions J'(x) O (a) Find lim f(x). x-1 05 01/1/20…

A: see below the answer and explanation

Q: The percentage of movie advertising as a share of newspapers' total advertising revenue from 1995 to…

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Q: 13. The function has the 1st derivative given by f'(x) = -x(x+3)(x - 1)²(x+4)³. What are the x…

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Q: A triangular plate with base 2 m and height 3 m is submerged vertically in water so that the tip is…

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Q: Find the Taylor series (general form) of f(x): 1 X centered at x = 1.

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Q: 6. Find a unit normal vector to the surface z = f(x, y) = xey - 2y at (0, 1, -1) and find an…

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Q: Solve: y (cosx)= (9+ y²)

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Q: (x) = x4−256x+4 Enter the x-values of any local minima, maxima, and inflection points.

A: Given f(x) = x4−256x+4

Q: Suppose a real number t determines the terminal point (a, b) on the unit circle as shown. (a,b) ▶ D…

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Q: 3) Solve the differential equaion (D2-4)y=e²-4

A: 3) The given differential equation D2-4y=e2x-4. We have to find the general solution of the…

Q: 6) as an ice black metts, the note at which its moss M, decreases is directly proportional to the…

A: according to bartleby guide line we do only first part of multipleplease re post other parts 6)…

Q: Differentiate. y' = y = 3 sec(x) - csc(x)

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Q: Use the power series method to solve the given initial-value problem. (Enter the first four nonzero…

A: The given initial value problem:x+1y''-2-xy'+y=0 ; y0=8 ; y'0=-1

Q: a building so that its foot moves away from the building at the note of 3 feet per second. When the…

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Q: 14. The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30…

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Q: 19. lim x²-5x-24 x-5 x²-9

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Q: Consider the following parametric curve. Answer parts a and b. x = 4+2t, y=1-6t; t = 2 a. Determine…

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Q: 1. Divide the interval [a,b] into n = 4 subintervals of equal length and compute A) the sum of the…

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Q: Find the average value of f on [0, 8]. YA 1 0 2 4 6 X

A: Given :- Find the average value of f on [0,8].

Q: Find the length of the spiral r=0², 0≤0≤ √21. The length of the spiral is (Simplify your answer.)

A: Topic = Integration

Q: You are given a feasible region. Find the maximum and minimum (if they exist) for the given…

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Q: Evaluate sin 5x cos 4x dx

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

Q: Use trigonometric substitution to evaluate the integral (a) arcsin(r)+C 9x 9 - x² √9-x² (b) 9x + C…

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Q: Consider the following functions. f(x) Find (f + g)(x). = g(x) = Find the domain of (f + g)(x).…

A: Domain of a function y=f(x) is the set of values of x for which f(x) is defined.

Q: 2 Find the area between the graph of y = 5 – 5x³ and x-axis and − 1 ≤ x ≤ 8 using properties of…

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Q: Q lan for the conic based Yon: Ellipse with major verti #) and a focus point at (9,4_ = sketch and…

A: SOLUTION: Given  that  an ellipse has major vertices at (-5,4),(11,4) And focus at (9,4) Now we have…

Q: The measurements of the base and altitude of a triangle are found to be 46 and 34 centimeters. The…

A: Given information altitude ( A ) = 34 cm Base ( B ) = 46 cm let Area = A

Q: Suppose a linear function has a vertical intercept at y = -9 and a horizontal intercept at x = 15.…

A: Linear equation