Differentiate the following and simplify. Show all work, thank you! Part ( a) and (b).

Q: Find the equation for the tangent line for f(x) = x² at x = 2.

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Q: dy Use implicit differentiation to determine given the equation xy + x¹ = e. dx dy dx =

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Q: How close does the line y = 6 + 2x come to origin? The closest distance the line y = 6 + 2x comes to…

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Q: Compare the graphs of y=f(x) and y= f(2x): A) y=f(x) is reflected in the y-axis  B) y=f(x) is…

A: To compare the graphs of .

Q: *A company manufactures coffee makers and has total revenue function R(x) = 39x -0.01x² where is the…

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Q: The partial fraction decomposition f(x) (x + 1) f(x)= g(x) + g(x) (x² - 4x + 7) 9 of where -4x² 16x…

A: The given expression is

Q: Find each derivative. Do not type any spaces. dr [10x²] [7] = d-8a] = [-5x² +14x - 9

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Q: Consider the following function and graph. y = 64 x² y 60 50 40 30 20 10 2 4 Use an iterated…

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Q: 1. Which of the following is not the sense of why there is a need for arbitrary constant? (a) to…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: please utilise implicit differentiation to calculate dy/dx if you are given:  a) (x^2)+(y^2)+xy=3…

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Q: Find the equation of the tangent line to the curve at the point corresponding to t π x = t sint y =…

A: x=tsin⁡ty=tcos⁡tProduct Ruleddx[f(x)g(x)]=f(x)g′(x)+g(x)f′(x)

Q: 2 √₁²x²3x dx

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Q: What is the coefficient of z in (+2x)"? Hint: Use the Binomial Theorem.

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Q: -5 (-2,9) (-1,-1) 30 20 10- 0 -10- (2.-7) The average rate of change from x= -1 to x= 5 is found…

A: Given graph:

Q: In a new card game, you start by paying $95.94. From a well-shuffled full deck of cards draw cards…

A: In a new card game, you start by paying $95.94. From a well-shuffled full deck of cards draw 3 cards…

Q: Find the length of the curve Arc length = F(t) = (et cos (), et sin (), ef ) for 0 ≤ t ≤ 3.

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Q: 2. The temperature T in degrees Fahrenheit, drops at a constant rate as the elevation, h in…

A: The temperature T is given by

Q: Solve the initial value problem y(t) = = dy dt Y t+1 + 4t² + 4t, y(1) = 8

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Q: g(x)=2x-5+1 h(y) = 2-y

A: g(x)=2x−53+1h(y)=2−y

Q: The function f(x)=√16 - 2x is continuous on the interval [0, 8]. Which number is its average value…

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Q: Identify the definite integral that computes the volume of the solid generated by revolving the…

A: Region is bounded by y=x3 and the line y=x, between x=0 and x=1Rotating the region about y-axis

Q: Part 2 (no Allar que = 10x7y - y, y(1) = - 3 = < Find the explicit particular solution of the…

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Q: (sinx-csc x) = A B C D 0 1 -cot²x 2 cot x

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Q: Write an equation for a sphere centered at the point (8,4,-3) with radius 7.

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Q: 1 1 A = +---- -28 and B= 4 55 55 -15 215 Are A and B inverses? O Yes, A and B are inverses. O No, A…

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Q: Set up an integral to find the area of the region above y = x² - 4x and below y = 2x ○ ſ₁¹ (2x − (x²…

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Q: The 3 x 3 matrix D is defined in terms of the constant k by D 2 k lk - 2 -1 3 4 2 3 J k+7] Given…

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Q: Let f be the function given by f (x) =−x³ + 3x² + 24x. What is the absolute maximum value of f on…

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Q: Show that the series converges by applying the Alternating Series Test: O O lim 148 1+ Inx (xlnx)2…

A: The given series .The aim is to check the convergence of the series.

Q: Let f be the piecewise function given above. The value of of A B 5 11 35 nonexistent f (x) dx is -1…

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Q: Find the local maxima and minima for the function. Find the intervals on which it is increasing and…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 25 + x² 5…

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Q: 19. x - y² +3=0, x-2y = 0.

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Q: Find the determinant of the following 4 x 4 matrix. Show all your work. 1025 |1 -2 0 5 3 2-6 -7 0 4…

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Q: Suppose your demand function is given by D(q) = − q² − 2q + 542, where q is thousands of units sold…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

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Q: X 1 2 3 4 5 y 12 -2 -3 -4 -5 -5 3 4 5 -4 -5 -5 -6 -6 -7 -8 -6-7-8-9-10 -8 -9 -10 -11 -12…

A: x∖y123451−2−3−4−5−62−4−5−6−7−83−6−7−8−9−104−8−9−10−11−125−10−11−12−13−14

Q: If y = 8 sin 2x cos 2x, then A 128 sin 2x cos 2x C. 64 sin 4x B. 128 sin 6x D. 8 sin 2x cos 4x

A: If , then to find .

Q: Consider the solid bounded by the plane sx=0,y=0, and x+y=2 along with z=4−x2. Find the volume of…

A: We have to find the volume of the solid.

Q: Consider the following autonomous first order equation: y' = ƒ (y) = (4y² − 36y +72) (4y² − 88y +…

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Q: Assume f(3) = 0, f'(3) = 6, g(3) = 1, and g'(3) = 3 f(x) g(x)* Find h'(3) given h(x) = A. -2 B. 2/2…

A: Given,

Q: Suppose that y = f(x) is a differentiable functio for which the following information is known: f(1)…

A: According to our bartleby expert guidelines only first three subparts are to be answered kindly…

Q: -2 -9 (8 +7t²) dt

A: I=∫−9−2(8+7t2)dt

Q: True or False, and explain why showing all steps. The function f (x,y) = x2 + y2 has a global…

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Q: nich step is part of finding the derivative of the function below? The Sice may not be in simplified…

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Q: Determine each feature of the graph of the given function. f(x) = - Answer Attempt 1 out of 2 Y =…

A: To determine the each of the feature of the graph of the following function.

Q: Use a right-hand rectangular approximate to estimate the area under the curve over the interval [0,…

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Q: Find the length of the spiral r=0², 0≤0s √5. The length of the spiral is. (Simplify your answer.)

A: Consider the curve

Q: The functions f and g have the values shown in the table and are differentiable. If A = f g, then…

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Q: Find the derivative of f(x)=-5x42x8. f'(x) =

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