You are given the graph of a function f. Determine the Intervals where f is Increasing, constant, or decreasing. (Enter your answers using Interval notation. If an answer does not exist, enter DNE.) -1 Increasing constant decreasing

Q: 3 Below is the graph of y =x. Translate it to make it the graph of y = (x+1)– 2. 中

A: We need to translate y=x3 to the graph of y=(x+1)3-2. That is, I'll shift the graph by 1 unit to the...

Q: 5. Let f(x, y) = x² + y? – xy + x. Find the critical point of f and determine if it is a local minim...

A: We will find the critical point for the given function.Also we will find that given function is loca...

Q: Find all values x= a where the function is discontinuous, For each value of x. give the limit of the...

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Q: A particle moves along the curve y=x3-x. If vx = 2 ft/sec and ax= -3 ft/sec2 as the particle passes ...

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Q: Find the linear approximation for f(x)=/1+ x at a=0. Use this linearization to approximate V1.1 O L(...

A: The linear approximation of f(x) at x= a is given by L (x) = f(a) + f '(x)(x - a)

Q: The monthly revenue R (in dollars) of a telephone polling service is related to the number x of comp...

A: Solution is written in below steps.

Q: tan? y dx = sec2 x dy %3D

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Q: Check the differentiability and continuity of the function below.: 3x 1. f(x) = 2. f(x) = 5- x² at x...

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Q: Find // y dV, where E is the solid bounded by the parabolic cylinder z = x? and E the planes y 0 and...

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Q: Given the function g(x) = 8x° – 60x + 96x, find the first derivative, g'(x). g'(x) = Notice that g'(...

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Q: 3. Let f(r, y) = y²x – yx² + xy. Find all critical points of f.

A: We have to determine critical points of f 

Q: Implicit differentiation

A: Given that: 1. 2x3y+3xy3=52. x2=x+2yx-2y3.xy-4y=x           NOTE: As per our answering guidelines, w...

Q: Evaluate the integral. 8 r log 4(x + 8) x +8 xp-

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Q: dy Find dx for the equation xy + sin(x + y) = 123643543 dy -y dx x+cos(x+y) dy -y-cos(x+y) da -cos(r...

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Q: Find an arc length L of the curve given by r(t) = ⟨2 + cos 3t, 3 − sin 3t, √ t^3⟩ for 0 ≤ t ≤ 5 exac...

A: The arc-length formula is: L=∫ab(x'(t))2+(y'(t))2+(z'(t))2dt...(1)

Q: QI Evaluate 2 2 || 2y2 sin(xy) dydx (2 0 x

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Q: Use the cylindrical shell method to find the volume of the solid obtained by rotating the region bou...

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Q: 10. Solve for the derivative of y IMPLICITLY 22 + Væ³ + 2y= y²

A: Note: According to our expert guidelines only first individual question is to be answered, kindly re...

Q: 2 dse the Reimann Integral to evaluate S v'dv.

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Q: Consider the integral sin (5x). dx: Applying the integration by parts technique, let u = and dv = dx...

A: Given that the integral   ∫sin-1(5x) dx .      

Q: dp The logistic equation for the population (in thousands) of a certain species is given by = 9p - 4...

A: dpdt=9p-4p2To Find: a. Sketch the direction field.b.If the initial population is 2900 (p=2.9), what ...

Q: y' = x +6y

A: 1) Given y'=x+6y  

Q: fracd the AREA honded by a cylind rical asonolinecte P=2m b. 2. C.

A: Derivation of surface area of open cylinder:S =∫02π∫0h∫0r dr dh dθS = 2 π r h    For given coordinat...

Q: determine the number of cells after two hours.

A: Follow the procedure given below.

Q: The trough below is full of water. Recall that water has weight density 62.4 lb/ft³. 2 ft 5 ft 8 ft ...

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Q: coS X =dx sin? x

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Q: The base of a solid is the region in the first quadrant bounded by the curves below. 25y = 25 – x2 x...

A: Given : Base of a solid bounded by the curves 25y=25-x2 , x-axis ,and y-axis. In the first quadrant ...

Q: 3. f (x) = V1+ v1 – x 4. у %3

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Q: Computational: (1) Given the function y = x3 +3x + 1, answer the following items. a) Find the slope ...

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Q: Use the Reimann ntegral to evaluateS vdv.

A: In this question we have to find the Reimann Integral.

Q: 10. Solve for the derivative of y IMPLICITLY 22 + vx³ + 2y= y²

A: Topic =Derivative

Q: A. Evaluate each of the following definite integrals. 2 S (8x3 + 3x2) dx 1.

A: Given that:

Q: Solve sin 40 cos³ 0 d0

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Q: y tan x dx + In* ydy=0

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Q: Given the graphs of f(x) and g(x), determine the value of expressions below. y f(x) y = g(x) lim (f(...

A: From the given graph, we can find the following limits: limx→2f(x)=0  limx→2g(x)=0 limx→1g(x)=1 limx...

Q: Evaluate the following function. 1. f(x) = 5x³ find f'(2) 2. f(x) = x³ + 3 find f'(3) 3. f(x) = x3 -...

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Q: 4x3+3x2- 30x-33 da Consider the indefinite integral x2 - 9 Then the integrand decomposes into the fo...

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Q: y = In tan(x – A) +B

A: Some Important Formulas 1. ddxtanx = sec2x2. ddxsin-1x = 11-x23. sec2x = tan2x +1

Q: Read each item carefully and encircle the letter of your choice. 1. It refers to an extreme point on...

A: 1.     2.

Q: Determine the Laplace transform of f(t) = (5t^3)(e^6t)

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Q: 1. If ü= (2,-3), v=(1, -5), and w=(6, 2), determine the following: a) |ü +v| b) 3 ỹ -ū +w

A: a) u→+v→=(2,-3)+(1,-5)=2+1,-3-5=3,-8=32+(-8)2=9+64=73|u→+v→|=73

Q: Suppose that the total profit in hundreds of dollars from selling x items is given by P(x)=5x-5x+7. ...

A: Average rate of change of f(x) as x changes from a to b is given by, A(x) = [f(b) - f(a)]/(b - a)

Q: 2. Evaluate the following integral: 6/ dx x2 Hint: Use x = 3 cose.

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Q: Now recall the general version of the power rule, where n is any real number. d = nx" – 1 dx Applyin...

A: Basic derivative problem

Q: Find the partial sum S„ for a geometric series such that a4 = 162, a7 = 4374, and n = 8. %3D Sum =

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Q: coS X =dx sin? x

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Q: Part A A helicopter carrying Dr. Evil takes off with a constant upward acceleration of 6.0 m/s. Secr...

A:   Given: A helicopter carrying Dr. Evil takes off with a constant upward acceleration of 6.0 m/s2. S...

Q: A population of squirrels lives in a forest with a carrying capacity of 1200. Assume logistic growth...

A: NOTE: Refresh your page if you can't see any equations. . the logistic model is given by here carry...

Q: В. Transform the following equations into its general form. 1. 1)2 212 2.

A: Given that:

Q: For the function ƒ (x) = 1 – 1 / (x + 2)2 , find the following: ii ) ƒ ( x + k)

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