In which limits below can we use L'Hospital's Rule? 1- eª x+0 sin(6x) Olim lim I→∞ lim I→0 lim x →∞ x x + tan x sin x ex X

Q: Find the derivate of the function F(x) = x²(x²-8) a) C 2 6b) f(x) = (5x²³²-7) (6x + 1) F'(x) = c) 5…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Question 19 ( ) Let f(r) Inz for all z>0. Determine all intervals on which is decreasing.

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Q: = 4y cos(2x - 5y) at the point (5,2,8) Find the tangent plane to the equation z =

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Q: For what values of p does the following series n=2 (Inn)p-2 n converge or diverge?

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Q: Find the limit. lim 0-0 cos(0) 1 sin (0)

A: Given limit limθ→0cosθ - 1sinθ

Q: 6y' - 2y = xy¹, y (0) = -1

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Q: The graph of y = f(x) has f(5) = -3 and f'(5) = -3. Which of the following might be a graph of y =…

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Q: Find parametric equations of the line that contains the point P(3, 1,-2) and intersects the line L:…

A: The solution is shown below-

Q: The function f(x) = - 0.625x^3 + 16.789x^2 - 102.722x + 658.154 approximates the number of…

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Q: [√² √sec²z - 1

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Q: Q11 Compute (a) [3.14] = dx (b) Compute [54] = d 5-4x- dx 3

A: To compute the following. (a) ddx3.14 (b) ddx5-4x3

Q: Determine if the limit lim (1+5x) 1+0+ exists, and if it does, find its value.

A: Given: limx→0+1+5x12x

Q: (b) x = dx dt 1 sin7 (t³)

A: Given:- x=1sin7t3

Q: A circle is inside a square. The radius of the circle is decreasing at a rate of 4 meters per minute…

A: Need to find out the rate of changing of area outside the circle but inside the square changing.

Q: We need to minimize the cost (measured in units of $100,000) of the pipeline, C(x) = 20✔ 20 5 x +…

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Q: Find the average rate of change of f(x) = x² from x = 1 to x = 4. (a) 3 (b) 5 (c) 15 (d) 6

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

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Q: Assume that x and y are differentiable functions of t. For the following, find dx/dt given that x =…

A: given  x2+y2=136d dx(xn)=nxn-1d dx(constant)=0

Q: In (1 + x²) x-0 1 COS X 37. lim - x² - 4 x→2 ln (x - 1) 38. lim

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Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 4 sin…

A: By using the double integration to find the area of the plane region  enclosed by the curves. y=sin…

Q: Find dy/dx at the given point without first solving for y. xy2 125 at (5, 5) d 11

A: The given equation is: xy2=125 Use the Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g'

Q: x²-1 Evaluate the limit, if it exists: lim - a. does not exist b. 2 *1 X-1 C. 0 d. 1

A: We are required to evaluate:limx→1x2-1x-1

Q: ts) Let f(x) = 1. f'(x)= 2. f'(4)= 5x² tan(r) sec(x) Find the following:

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: Given function f( x ) = 36-x2

Q: Find an equation of the sphere with center  (3, −7, 3)  and radius 5. Use an equation to describe…

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Q: A solid is constructed so that one side is the region between the lines x = a, x = b, the graph of y…

A: Consider the given solid. We know that if the cross section is perpendicular to the x-axis and the…

Q: 2) Sketch the graph of a continuous function y = f(x) that satisfies the following (Identify any…

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Q: Find the future value of the following ordinary annuity. Payments are made and interest is…

A: Given : Find the future value of the following ordinary annuity. Payments are made and interest is…

Q: Let C(x) represent the cost of producing x units of a particular commodity where C(10)=1000 and…

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Q: The number of hits on a certain website​ (in thousands) is approximated by f(x)=30e^0.171x​, where…

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Q: Consider the function f(x) = 12x5 +75x¹ - 120x³ +1. For this function there are four important…

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Q: Given the vector u = (5, 3), find the magnitude and angle in which the vector points (measured…

A: u→=<5,3>

Q: An object traveling in a straight line travels s(t) kilometers after t hours, where s(t) = 8t² + 5t.…

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Q: Consider the following vector function. Find each of the following. r'(t) = = r'(0) r(t) = cos(t) i…

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Q: Consider the graph below. Which of the following is the interval [a, b] or the limit of integration?…

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Q: Given f(10) = 50 and f'(10) = 2 Approximate the following values f(11)~ f(9.5)~ ƒ(10.25)~

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Q: given by C(x) = -0.07x² + 75x. Find C(288) C(287) Interpret the result

A: we will find the required.

Q: Consider the center of mass of the following. A lamina occupies the part of the disk x² + y² ≤ 9 in…

A: The solution is shown below- As per company guidelines only first three parts are allowed to solve.…

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

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Q: K For the following demand function, find a. E, and b. the values of q (if any) at which total…

A: Given p = 700e-0.2q

Q: Consider the curve 1x² - 4xy – 2y³ = 290.25. (a) Find an expression for y'. y' = = (b) P(-13.5, 3)…

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Q: 16. A limit exists if both the right-hand and left-hand limits are equal. 17. A jump discontinuity…

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Q: Evaluate the limit using L'Hospital's rule if necessary lim (1 + 4) * I→∞

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Q: An open-top rectangular box is being constructed to hold a volume of 350 in³. The base of the box is…

A: Given: volume = 350 in³ base material costing = 6 cents/in² front cost = 12 cents/in² remainder…

Q: 14. The domain of the function is y 4 2 -4-20 2 4 x

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Q: Determine an expression for the derivative of this function. (Do not simpli f(x) = (2x²-x)(√√x² - 1)

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Q: Find the points on the cone ² = x² + y² that are closest to the point (5,4,0)

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Q: A water well has an 8-inch diameter and is 180 feet deep. The water is 15 feet from the top of the…

A: Given: Pumping the well dry which is 8- inch in a diameter 180 feet deep for which the water is 15…

Q: find a reduction formula for the integral|x" cos x dx.

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Q: A chemist has three different acid solutions. The first acid solution contains 15% acid, the second…

A: A chemist has three different acid solutions. The first acid solution contains 15% acid, the second…