) Show that the gradient of a scalar function f is a vector along the normal to the level rface whose magnitude is the greatest rate of change of f.

Q: 15? - 17 What is the exact value of sin (cos-le) where e = Provide your answer below:

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Q: Solve the following using a +/- table, making all of your thinking visible (r-2) (x+1) (4-x)(x+5) > ...

A: Find your answer below 

Q: Consider the series. 00 9n Σ 3/5 n=1 (n2 + 1) 9x Let f(x) = Find f' (x). 3/5 (x² + 1) (Express numbe...

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Q: sec® x dx cot x SE V

A: We can evaluate the given integral by using the substitution u= tan x and the following formulas. 1...

Q: You are designing a poster which has a border around the printed portion. The border is 2 inches wid...

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Q: 2. H(x) = 4x2 + 4x - 4 %3D Circle the correct choice: Concave up or concave down? Vertical Stretch, ...

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Q: 4 z = lim f(x) y 1 2 3 4 2.

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Q: You are designing a poster which has a border around the printed portion. The border is 2 inches wid...

A: Given:  The border is 2 inches wide on the left and right sides, 3 inches wide on the top and bottom...

Q: ACTIVITY 1 onl Direction: solve and analyze each of the following problem in neat and orderly manner...

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Q: Find the average value of the function f(x) = x- 2x +1 on the interval [-1, 3]. %3|

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Q: Internet Audience At the end of a certain year, the four companies with the largest number of home I...

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Q: Find the limit. est – 1 lim t-0 sin(t)

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Q: (a) Evaluate sin 2z -dz, 3z -ĝi where C is an anticlockwise unit circle centred at the origin.

A: Follow the procedure given below.

Q: The transformation of a function f(x) into a function g(x) is given by g(x) = Aƒ(Bx + H) + K. where ...

A: Topic = Function

Q: gent subsequer O an = (-2)" O an = 1+ (-1)" · 10(-1)"-n n sin () %3D O an = O an = 1+2· (-1)"

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Q: A company can sell x units of a product when the price is p = D(x) = 3.00 – 0.002x dollars. The tota...

A: Given , No of unit =x Price=p Also given P=D(x) =3.00-0.002x and C(x)=0.006x2+0.52x+270 Hence,    

Q: If the limit of f(x) is 5 and the limit of g(x) is 2 as × approaches a constant k, what is the limit...

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Q: 4) Determine whether the integral converges or diverges, and if it converges, find its value. - dx (...

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Q: ate the integral. (If the quantit 8. dx (x2 + 4)2

A: The given integral,                ∫-∞∞xx2+42dx

Q: Find the slope and y-intercept (if possible) of the line. (If an answer is undefined, enter UNDEFINE...

A: The given line equation -x+y=8

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Q: cos x dr 4 sin x

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Q: хр x?V25 - x

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Q: Find the indefinite integra

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Q: Consider the differential equation = (3 - y)cos x. Let y = f(x) be the particular solution to the di...

A: The given differential equation is: dydx=3-ycos(x)

Q: 6. dx Vx - 1

A: Given that I=∫161x2-1dxsolution :∫1x2-a2dx=logx+x2-a2+C∫161x2-1dx=logx+x2-116=log6+62-1-log1+12-1=lo...

Q: 4 - 3 + – Find the limit of f(x) = as x approaches o and as x approaches - ∞o. 9. 9 - X

A: Find the limit of the function .

Q: 1. Differentiate each of the following with respect to x (find y' =2). Do not simplify your answers ...

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Q: Integrals of the form sin mx cos nx dx sin mx sin nx dx cos mx cos nx dx can be found using the foll...

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Q: Evaluate the integral. Show all your work. dx (x² – 1)3/2

A: Given that: ∫dx(x2-1)3/2

Q: Find the equilibrium point for the supply and demand functions below. Enter your answer as an ordere...

A: The supply and demand function,Sx=4x2+11x+43Dx=115-x

Q: In the 1990s, significant numbers of tourists traveled from North America and Asia to Australia and ...

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Q: Put the function P = 8(1.8)' in the form P = Pekt. NOTE: Round your answer to four decimal places, i...

A: The objective of the question is rewrite the given function in different form.

Q: Write the equation of the line tangent to the graph of y2 = 6y-4x+3 at (-1,-1).  The equtaion is y=...

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Q: Use the rules of differentiation to find the derivative of the function. f(x) = V f "(x) )%3D

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Q: Francine currently has $45,000 in her 401k account at work, and plans to contribute $3,000 each year...

A: We need to find total amount accumulated.

Q: 6. The limit of that constant is that constant. 7. The limit of a constantc times a function is equa...

A: Since we are given with the multiple number of questions and our guideline is solve the problem only...

Q: substitution to convert the integral to an integral of rational functions. Then use partial fraction...

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Q: can

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Q: Evaluate the integral. (If the quantity diverges, enter DIVERGES.) ∞   0xe−x dx

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Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not evalua...

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Q: SOLVE the following DIFFERENTIAL EQUATIONS. 1. cos'x sin x dy + (y cos²x – 1) dx = 0 2. xy' =2xex - ...

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Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) f(x...

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Q: x' +2y² Show that does not exist. lim (x.y)-0,0) 2x

A: Along y = x:     limx, y→0, 0x2+2y22x=limx→0x2+2x22x=limx→03x22x=limx→03x2=0

Q: Find the slope of the tangent to the curve, y = 2x – x² +x° at (0,2).

A: Given curve is  y=2x-x2+x3.  We have to find slope of the tangent to the curve , at (0,2 ). To find ...

Q: The transformation of a function f(x) into a function g(x) is given by g(x) = Af(Bx + H) + K. where ...

A: topic - translation of a function

Q: Find the average value of the function f(x) = x³ – 2x +1 on the interval [-1, 3].

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Q: Rewrite the integral in the 5 other orders. Explain your answers. 2 4-y2 f(x, y, z) dz dy dx

A: The given integral is ∫x=0x=1∫y=2xy=2∫z=0z=4-y2fx,y,z dzdydx. The domain of integral is R=x,y,z: 0≤x...

Q: Consider the equation (y² + xy³) dx + (5y² – xy + y³ sin y) dy = 0 • Show that the original DE is no...

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Q: Let g(x) = x². Which of the following outputs of g is not guaranteed by the Intermediate Value Theor...

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