Evaluate the following. 3. lim (x³ + 3x² + 1) X-2 4. lim v2x +5 X-2

Q: For the following functions y = f (x), find f ′ (a). f (x) = 3x2 − x + 2,      a = 2

A: Given:        f(x) = 3x2-x+2    Differentiating with respect to x, we get       f'(x) = ddx3x2-x+2  ...

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Q: Let f(x) = V13 – x. Compute f'(4) using the limit definition f'(4) =| Find an equation of the tangen...

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Q: Provide an appropriate response. Given fx) dx = 4 and g(x) dx = 2. use properties of definite integr...

A: We have to solve the integration

Q: CoS y By-2) dy

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to g...

Q: Consider the following curve. RO) = Determine the domain of the curve. (Enter your answer using inte...

A: Given f(x) = x-3x2  to find local minimum values, find the values of x when f'(x) = 0

Q: 1. Find the equation of the parabola given the following parameters and draw the graph of the equati...

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Q: d'y dy and dx 2. Find by implicit differentiation. dx? 5xy? = 1

A: The given function,    5xy2=1

Q: questions

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Q: 9tind the voleime of the s0lid generated by revolving the region bounded by the given lines and curv...

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Q: (a) Sketch the region bounded by the graphs of y = x + 1, y = x2 – 1, x = 1, and x = 2. %3| %3D | (b...

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Q: a) f(x) is a polynomial function. If f'(x) has a degree of 7, what is the degree of f(x)? b) Write a...

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Q: X dx У3— 2х — х2 - Hint: Complete the square for the denominator for part c.

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Q: la) Find the area of resion between two functions.

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Q: Let f(x) = V43 – ¤ %3D The slope of the tangent line to the graph of f(x) at the point (7, 6) is The...

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Q: . Find a formula for the inverse of the function and show that fif'(x))=f'(fx)). 4х-1 a. y = V10-3x ...

A:  Note: - “Since you have posted a question with multiple sub-parts, we will solve the first three su...

Q: 5. prove thatS" erf (x) dx =o CA

A: ddx(erf(x)) =2 e-x2π   I =∫-aa erf(x) dxI= erf(x) x -∫ ddxerf(x) x dxI = x erf(x) -2π∫ x e-x2 dx-x2 ...

Q: A manager of a store that sells and Installs spas wants to prepare a forecast for January, February,...

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Q: find deriva tve fla)= (e^+フス?) 3 ,2 -2 X -4メ ² + 5x +12)

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Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1 + x 4 %3D 00 f(x) =...

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Q: You decide to begin selling light sabers at the local fair. Your cost for each light saber is $1.03 ...

A: Given query is to find find the cost function, revenue function and unit required to be sold to make...

Q: Which of the following integration expression can be transformed into integral of power (Ju"du). (c ...

A: A

Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) = n = = 4, c = 5 x2' Pa(x) = ...

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Q: f (x) %3D х7 + 9х3 — 2

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Q: find f ′(x) for each function. f (x) = 4x2 − 7x

A: Given :f(x)=4x2-7xformula using : ddxxn=nxn-1

Q: find f ′(x) for each function. f (x) = 5x3 − x + 1

A: Let's find. 

Q: Match the following integration expression on the left with an appropriate form of its Antiderivativ...

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Q: Find f'(-4) if f(x) = 4x. 3 f'(- 4) = (Simplify your answer. Type an integer or a fraction.) Туре

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Q: What is the area of the shaded region? y = sin x TT ST 6

A: From the given region; So, The point of intersection between the curve and line is: y=sinπ6=12y=sin...

Q: Question 2 Provide an appropriate response. Can (x6 + 8)- dx be integrated with u = x6 + 8? Explain ...

A: The given integral is (x6+8)2.

Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection wi...

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Q: Activity 1. In this ULO, we have leamed how to use critical points, first derivative test and second...

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Q: The limit below represents the derivative of some function f(x) at some number a. 10 sin(2 + h) – 10...

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Q: 17. The graph of the function fon the interval -4 sxs 7 consists of three line segments and two semi...

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Q: Find the arc length made by a central angle of pi/4 radians and a radius of 10 cm.

A: Given problem:- Find the arc length made by a central angle of pi/4 radians and a radius of 10 cm.

Q: The following two functions represent the value of two stocks. G(t) represents the value of GeniusMa...

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Q: coth (7x - 3) + C B) tanh (7x - 3) +c I sech? (7x - 3) + C tanh (7x - 3) + C

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Q: Question 8 Which of the following is NOT EQUAL to the given integral. tanx There is no correct answe...

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Q: Graph of f The graph of the function f shown above has horizontal tangents at x = 2 and x = 5. Let g...

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Q: 3x + 11 19. Which of the following are equivalent to da ? a + 2 L(3z+11)dz L(+2)dz 5 I. 3 + z + 2 m....

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Q: . Find the length of a radius of a circle with a central angle of 3pi/5 and an arc length of 24pi/5.

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Q: Consider the function. f(x) = -2x3- 12r2 - 24x 15 Step 2 of 2: Determine the open intervals on which...

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Q: For vectors ā = (2,4,-1), b =(-1,3,2), calculate the vector projection of b on ā. %3D

A:  Vector projection of b→on a→=(a→.b→)a→Consider  a→.b→=(2×(-1))+(4×3)+((-1)×2)                      ...

Q: 3. [xsechtr'dx 5. (secht2tdt

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Q: Consider the series 00 1 Σ n4 + 3n n=1 Complete the following application of the Comparison Test to ...

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Q: 1. lim f(x) = -1 and f(1)DNE 2. lim f(x) = 1 and f(0) = -3 x+1 3. lim f(x) = -2, lim f(x) = 2 and f(...

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Q: find derivative fx)= tan (x) x2 + 1 川

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Q: (1+,x£)u[ = (x)f I 'I %3D ,find f'(x). V(4x3 – 5x)2

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Q: 9. Use the table below to answer the question. School Population By Gender Males Females Total Fresh...

A: topic - probability note : as per bartleby guidelines, we are supposed to answer only first question...

Q: Sketch the region enclosed by y = 3x and y 5x2. Find the area of the region.

A: The region is enclosed by y=3x and y=5x2