Given the function: f(x) = 47' - 8z 9x' + 8x2 + 8x - 4

Q: If f is decreasing on (a, b), then f ' (x) < 0 for each x in (a, b).   a) True b) False

A: We know that the function is said to be decreasing on I then f′(x) &lt; 0 at each point in an…

Q: Let u = (-3, 2), v (0,-1) and A = %D %3D %3D NOTE: Give ezact answers. (a) Find ||u|| relative to…

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Q: Let y = sin(2x). If Aa 0.3 at a 0, use linear approximation to estimate Ay Ay = Find the percentage…

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it…

A: Given query is to find the value of the integral.

Q: A fence is to be used to entirely enclose a rectangular plot of land with an area at 1600 ft.² It…

A: To show that a 40ft by 40ft rectangle will require the least amount of fencing to enclose the given…

Q: If f(x) = (3x² – 8) (5x + 4), find: f'(1) =

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Evaluate the double integral // fO f(r, 0) dA. T/6 (4 r2 sin(0) cos(0) dr de Sketch the region R.

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Q: Find a power series for the following function and determine the center and the radius of…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: S x²(csc2x³)(cot2x³)dx

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Q: Solve the initial value problem. x2у" - 4хy' - бу%3D 0, у(1) %3D з, у'(1) %3D 4

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Q: Find the absolute extrema of the function on the closed interval. g(x) = 9 sec x, 3 minimum (x, y) =…

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Q: ind, if any, the local maximum and minimum values and the saddle point(s) of the function f(x,y) =…

A: To find, if any, the local maximum and minimum values and the saddle point(s) of the function fx,…

Q: Question 12 Find the derivative. y = 126x A (72 In 12)126x B (12 In 6)126x (C) (72 In 6)126x D (6 In…

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Q: 6 Tangent Line. If p(x) = 5x² + 5x4 + 4 %3D Then the equation of the tangent line to the function…

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Q: Find the slope of the tangent line to the curve at the point (1, 0).

A: Given, f(x)= x-x³ (1,0)

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

A: Given;  Minimize :(x, y) =x2+y2 Constraint: x+2y-20=0.

Q: Find all horizontal asymptotes for f(x) Vx2+3 %3D

A: Solve the following

Q: Finding an Equation of a Function  Find an equation of the function f that has the given derivative…

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Q: Let å = - 5i – 43 and b = - 7ỉ + 23. Find ä · 6

A: This question can be solved using the concept of dot product.

Q: Vtan(7x) sec?(7x) dx

A: Given query is to find the integral of the expression.

Q: 3x – x² + 12x – 4 lim - 3x+ – x³ + 3x² + 2x – 1

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Q: Question Consider the function f(x) = 2 tan (x) – 3 over the interval Does the extreme value theorem…

A: Given function f(x)=2 tanx -3     ;  -π3 , π3

Q: in 5-- 2 34 6. Graph of f The graph of the function f is shown above. Which of the following…

A: here we can see than the f(x) is discontinue at 4  so if function is discontineous it means the…

Q: 3 Consider the function f(x) Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(æ) =…

A: Here, the given function is: f(x)=5x3-3x6

Q: Solve the initial value problem  y" + 8y' + 25y = 0 ; y(0) = 1, y'(0) = 2

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Q: Consider the sequence {10, -2, ) Find a formula for the general term an of the sequence, assuming…

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Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder r? + y? 64 and…

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Q: Trapezoidal Rule. Use the Trapezoidal rule to approximate the integral — 2х dx with n = 4…

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Q: A ball is being inflated such that the volume is increasing at a constant rate of 100cm3/s How fast…

A: Given  and

Q: */2 2 cosx dx 1+ (sin x)2 -n/2

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Q: 4 The line y= -Lx+3 has a perpendicu lar which fangent to the graph of y= (x²-2) (2x+k) at x=-l,…

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: Betermine whether the Mean Value theorem can be applied to f on the closed interval [a, b)]. (Select…

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Q: Match the following series with the series below in which you can compare using the Limit Comparison…

A: As per guidelines, I can answer maximum three subparts of a question. Since you have asked for…

Q: If f(x) = (1 − x)2 and g(x) = 8 − x, find f(g(x)) and g(f(x)) f(g(x)) = g(f(x)) =

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Q: True or False: For the shell method V = T p (x) h (x) dæ False, this is the disc/washer method True,…

A: This question is based on shell method.

Q: The r.m.s. value of f(t) V2x – 1 across [-2,1] is Answer:

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Q: at = 5? What is the instantaneous slope of Y = %3D - 25 25 15

A: A detailed solution is given below

Q: 4) With respect to the origin 0, the points A and B have position vectors given by OA = i+ 2j + 2k…

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Q: biscee HOM VIT MOBKI (-) = (x)f %3D (x? – 7x+13) for 8. Identify any asymptotes, extrema, points of…

A: Given that the function is       f(x) = (x2-7x+13)/(x-4)

Q: Use the properties of logarithms to expand log Each logarithm should involve only one variable and…

A: The objective of the question is expanding the given function.

Q: O EXPONENTIAL AND LOGARITHMIC FUNCTIONS Table for an exponential function The function g is defined…

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Q: 16. Find the number of units x, measured in thousands, that will minimize the average cost function…

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Q: Object Height. Suppose an object is thrown straight up from the ground. The height after t seconds…

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Q: Find the taylor series for f(x) about x=3 15) f(x)=x^3-10x^2+6

A: This question can be solved using the concept of expansion of Taylor series.

Q: 5æ")". 10 Differentiate f(x) = 5(3x" You do not need to expand your answer.

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Q: omposition. Suppose we want to find the composition of a function with itself. Let g(x) = -4(x+3)2…

A: Given, g(x)=-4(x+3)2

Q: 3x2 — 9х + 11 2х + 4

A: Given query is to find the derivative.

Q: 7ェ +8 If f(x) = find: 4x +3 f'(x) = !! f'(4) =

A: The objective is to find f'(x) and f'(4).

Q: Integration by Substitution. The rate of growth of Grass carp, one of the most common type of fish,…

A: Given integral ∫13 2x+6x2+6x+2 dx