Evaluate the limit using L'Hospital's rule if necessary lim (1 + 12) ² €-8

Q: Use Fubini's Theorem to evaluate the double integral ſf f(x, y) dA, where f(x, y) = −3x − 4xy – 9y²…

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Q: 4 (b) Σ(-3)3k k=1

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Q: The marginal cost of manufacturing a yards of a certain fabric is C'(x) = 3 – 0.01x +0.000006x² (in…

A: We need to find the increase in the cost if the production level is rasied from 3000 to 8500 yards.…

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = −20t³ + 60t.…

A: A particle moves along the x-axis so that at time t > 0 its velocity is given by v(t) = −20ť³ +…

Q: Consider the region bounded by the curve y = 27x − x4 and the x-axis.  Find the exact area of the…

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Q: 4. How far from y-axis is the center of the circle 2x² + 2y² + 10x - 6y - 55 = 0? 5. How far from…

A: Given the equation of a circle, 2x2+2y2+10x-6y-55=0

Q: Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the…

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Q: Which of the following shows the simplified function of cscxsin 01 -1 tan x O cotx

A: Topic - Trigonometry We are given, csc x sinπ2-xWe know that,sinπ2-x=cos(x)

Q: can you please write out the final answer as its supposed to go in the answer box because I cannot…

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Q: Find the absolute maximum and absolute minimum of the function f(x) = = 3x² + 5x + 4 over the…

A: The objective of the question is determine the absolute maximum and minimum of the given function.

Q: A surveyor wants to know the length of a tunnel built through a mountain. According to his…

A: A surveyor wants to know the length of a tunnel built through a mountain. According to his…

Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

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Q: Determine the value of (gof)(-1) when x+3 f(x) g(x) = x² - 1. T

A: Topic = Functions

Q: (³ a sin 3a da.

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Q: 5. What is the length of latus rectum of a parabola with an equation 3x2 + 8y = 0?

A: Note: as per our answering guidelines we should solve only one question. So i am solving one…

Q: If f(x) + x²[f(x)]4 = 18 and f(1) = 2, find f'(1). f'(1) =

A: As we know that ddx(fg)=f'g+fg'  for two function f and g of x.see below the calculation and answer

Q: Refer to the figure and find the volume V generated by rotating the given region about the specified…

A: Let's find volume when R2 rotated about AB line.

Q: Solve the inequality (z - 4)(x − 3)² 4 0x3

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Q: If z² = x³ + y²₁ dt dx dt Please give an exact answer. || - Provide your answer below: - dy 2, = =…

A: Topic = Derivative

Q: Which of the following are rational functions? Select all that apply. f(x) = = Of(x)= Of(x) = Of(x)…

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Q: 1. Consider the function f(x)= x-x5 + sin(27(x - 1)). Use the MVT to prove that there exists a c…

A: Use mvt

Q: If f(x) + x²[f(x)]4 = 18 and f(1) = 2, find f'(1). f'(1) =

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Q: A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall…

A: A cat falls from a tree at time t = 0. v(t)=-32t ft/s

Q: Refer to the figure and find the volume V generated by rotating the given region about the specified…

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Q: A kite flying in the air has a 96-ft string attached to it, and the string is pulled taut. The angle…

A: Topic = Trigonometry

Q: Chapter 6 11) Find the product (3 + 3x) (-4 + 3x)

A: Topic = Algebra As per guidelines , At a time only one question can be answered. Please repost for…

Q: Find the area of the shaded region. 74 +3 sin(e) 0 414 D-1 41 2 32 2 41 2 EN

A: Topic = Area

Q: f(x) Consider the function h(x): x+1' Give the formula for the derivative h'(x).

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Q: HOMEWORK NO. 1 (A) Eliminate the arbitrary constants. 1. xsiny + x²y = c 2. ax² + x + y² = 0 3. y =…

A: We have to eliminate the arbitrary constant from the given expressions

Q: The crash risk of an intoxicated driver relative to a similar driver with zero blood alcohol is…

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Q: Consider the following. 7x8+y³ = 5x (a) Find y' by implicit differentiation. y' = (b) Solve the…

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Q: Find the equation of the tangent line to the curve y = 10x -x^2 at the point x =1

A: To find the equation of the tangent.

Q: 1. Given a. b. ( C. f(x) = 10x5 4x + 5 and g(x) = 2x + 1. Find and simpify fog(x). ) Compute…

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Q: How might I use spherical coordinates to find the volume of a ball with radius R to prove this…

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Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = [1,…

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Q: Solve the following exponential equation. Express the solution set in terms of natural logarithms or…

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Q: Two long straight roads, one running East-West, and the other running North-South meet at a point O.…

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Q: 4. Carry was given a 200-peso gift card for her birthday. She plans to use it to buy new ball pens…

A: Let the number of pens she bought =x

Q: 1 X "S “Ţ (x² + y2) dzdydx 04 12 O ! 11 60 3 20 O-11 60

A: Given, ∫01∫0x∫1yx2+y2dzdydx

Q: Complete the table shown to the right for the population growth model for a certain country. k=…

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Q: Consider the space curve r(t) = (3 sin(- 4t), cos(-4t), 2√2 cos(-4t)). a. Find the arc length…

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Q: ans against the side of a house. The angle of elevation of the ladder is 66°, and the top of the…

A: Given query is to find the length of the ladder.

Q: Evaluate the integral. √√225-1² dt √√225-1² dt =

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Q: า es of p is the series below divergent? rect answer below: n=1 (-1)+¹(In (4n+5))²

A: We have to find the value of p such that the given alternating series is divergent.

Q: -1 tan¹ n n

A: NOTE: Refresh your page if you can't see any equations. . find the limit of the sequence

Q: A particle moves along the x-axis so that at time t> 0 its position is given by x(t) = t4 - 18t² –…

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Q: A particle moves along the x-axis so that at time t≥ 0 its velocity is given by v(t) = 3t² − 48t +…

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Q: 3 (x-2) y'= y + 2(x-2)

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Q: Solve the exponential equation by expressing each side as a power of the same base and then equating…

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Q: 6:33 A particle moves along the x-axis so that its velocity at time 0 < t < 18 is given by v(t),…

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