In which limits below can we use L'Hospital's Rule?

Q: Instagram has a revenue function of R(q) = 5q 2 − 10q+ 600 and a cost function of C(q) = 3q 2 + 200,…

A: Note: As per our guidelines, we are supposed to answer only one question with a maximum of three…

Q: The radius (R₁) of one ball bearing is 1.0 mm greater than the radius (R₂) of a second ball bearing.…

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Q: Suppose that f is differentiable at 1 and f'(1) = 1 = f(1). Evaluate lim xf(x²+x-5)-16 22-4 (Hint:…

A: Given f is differentiable at 1 f'(1)=1=f(1) We are required to find limx→2x4fx2+x-5-16x2-4

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

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

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Q: Find the area of the surface obtained by rotating the curve y = √2x from x = 0 to x = 7 about the…

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Q: The tangent to (2,4) on the graph of a function f(x) is y = 5x - 6. Evaluate f'(2). (a) 5 (b) 4 (c)…

A: We have given the equation of tangent line y=5x-6 of f(x) at point (2,4).

Q: Sketch-the-graphs-x = 4y - y² and x = y

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Q: Consider the following problem: a farmer with 650 feet of fencing wants to enclose a rectangular…

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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: In this problem, p is in dollars and q is the number of units. Suppose that the demand for a product…

A: Given: Demand for product is given by 2p2q = 30000+9000p2, where p is in dollar and q is the number…

Q: п Convert the point (p, 0, 0)=(3, 377) 6 expressions, or decimals to at least one decimal place. (x,…

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Q: The Fourth Gate You arrive at the fourth gate, feeling confident in your skills. "It is a good thing…

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Q: Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and…

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Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: Given:  fx=2-62x To Find:  To determine the domain of the derivative of fx and  then to evaluate it…

Q: Given f'(x) = -9 sin(3x) and f'(0) = 2 and f(0) = 5. ƒ(7) Find f =

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Q: Flow of Water from a Tank Water flows from a tank of constant cross-sectional area 40 ft² through an…

A: We have to find the rate of decrease of height.

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Q: Sketch the region of integration and convert the polar integral to a Cartesian integral or sum of…

A: Please see the below picture for detailed solution.

Q: Consider the function f(x) = 12x³ +30x¹ - 160x³ +4. f(x) has inflection points at (reading from left…

A: Application of Derivative

Q: For the following function, a) give the coordinates of any critical points and classify each point…

A: As per rule I need to solve only first three subparts.

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Q: Find the surface area of revolution about the x-axis of y = 5 5 ㅠ 0 ≤ x ≤ 5 sin(5x) sin(5x) ov over…

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Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, and y = 0,…

A: Given: y = 4x2 x = 1  y = 0 about x-axis

Q: Let y = f(x), where f(x) = (5x² + 6)1/3. Find the differential of the function. dy =

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Q: Answer the following True or False. If f(x) is a positive 1-1 function with inverse f−¹(x) with f(a)…

A: Given:-fx is a positive 1-1 fuunction with inverse f-1x with fa=c,fb=dthen π∫abfx2dx=2π∫cdyb-f-1ydy

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: Find the tangent plane to the equation z = -4x² + 3y² - 5y at the point (3, 2, -34)

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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,…

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Q: Determine if the function f(x) = r²-3x+2 satisfies the hypotheses of the Mean Value Theorem (MVT) on…

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

Q: A ball is thrown upward in the air, and its height above the ground after t seconds is H (t) = 75 ⋅…

A: Given  height above the ground after t seconds is H(t)=75t - 16t^2 feet. To find the time when the…

Q: The Third Gate You arrive at the third gate and look for the inscription. Your computer translates…

A: For x approaching c from the left, x<c  ⇒  x-c5<0The denominator is a negative  approaching…

Q: If is differentiable, then the function. e + f(x) √√3 is differentiable.

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Q: Average Cost for Producing MP3s The average cost (in dollars) incurred by a media company each week…

A: Here is the solution:

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: The sum of integrals below give the area of a region in the xy-plane. Sketch the region, label each…

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Q: The Sixth Gate After walking through the fifth gate, your computer informs you that more than half…

A: Given function f( t ) = 1a( 7t3 - 55t2 + 165 )40

Q: S2x√6x- 6x-x² dx =

A: To find out the integration of the given expression.

Q: Suppose a product's cost function is given by - 3q² + 800q, where C(q) is in dollars and q is the…

A: The details solution of the given question is given below in step 2.

Q: Find the volume of a pyramid with height 28 and rectangular base with dimensions 5 and 7 using…

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Q: 2y-³ Find the maximum rate of change of the function f(x, y) = X at the point (1,5)

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Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given differential equation:- x2+y28dy=7xdx+ydy

Q: [√² √sec²z - 1

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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 tangent plane to the equation z = 7e²²-2y at the point (4, 8, 7) 2 II

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Q: Answer the following questions. 1 A function f is given by f(x) = (x+1)|x+3| x+3 (a) Express f(x)…

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