Use algebra and limit laws to find the following limit if it exists. If it does not exist, explain why. Show intermediate steps. (2+ h)² + h − 4 h lim h→0

Q: For the graph f(x) above, find: Find: lim f(x) = x→6- lim_f(x) = x→6+ lim f(x) = x→6

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Q: 6. (D² + 1)y = 10e* sin x

A: see below the answer and explanation

Q: The monthly profit from the sale of a product is given by P = 32x - 0.2x² - 150 dollars. (a) What…

A: We have given monthly profit  P=32x-0.2x2-150 Differentiating profit function with respect to x  P'…

Q: A closed rectangular container with a square base is to have a volume of 2304 in³. The material for…

A: The following formulas of derivatives has been used to solve this…

Q: A = {1, 2, {3,4}, {5, 6, 7}} Select the correct value for |A|. A) 4 B) 5 C) 6 D) 7

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Q: Te ex (ex - 7)(ex + 1) dx

A: The given integral is ex/[(ex-7)(e2x+1)].

Q: A typical cup of coffee contains about 90 mg of caffeine and every hour approximately 12% is…

A: Given a typical cup of coffee contains about 90mg of caffeine and every hour approximately 12% is…

Q: 1 7. For f(x) write the linear approximation at a = 0 and estimate f(-0.1). (Note: The derivative of…

A: Let's find value of f(-0.1).

Q: Find the limit. (If an answer does not exist, enter DNE.) x² - 6x + 8 X-4 lim X→ 4

A: To evaluate the following limit. limx→4 x2-6x+8x-4

Q: 50'-0" 25'-0" ONE DIMENSION: What is the perimeter (linear footage) of this concrete slab?

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Q: 2. Find the dy/dx by implicit differentiation. a. (sin(x) + cos (лy))² = 2 b. cscx = x(1 + tany)

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Q: 10+ 9 8 7 6 5 4 3- 2 1 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3- -4 -5 -6 -7 -8 -9 -10+ 1 2 3 4 5 6 7…

A: Graph of the function is given, we have to find the values of…

Q: The answer does not match the alternatives. Which would be? a) 3x-2t b) x²+3t² c) 4x-t d) 3x + t…

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Q: sin ln x X dx = (

A: formula used is d dx(lnx)=1x∫sinxdx=-cosx+c

Q: Let lim f(x) = 6 and lim g(x) = 12. Use the limit rules to find the following limit. X-5 X-5 f(x)…

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Q: Solve the following system of linear equations by using the inverse matrix method. x + 2y -z = -4…

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Q: Find an equation of the tangent(s) to the curve at the given point. Then sketch the curves, and…

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Q: Suppose a company has fixed costs of $36,000 and variable cost per unit of +222 dollars, where x is…

A: Given that fixed cost is $36000 and variable cost is 13x+222 dollar per unit.And selling price per…

Q: A car rental agency charges $100 per week plus $0.10 per mile to rent a car. a. Write an equation…

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Q: Camels have been reported to drink as much as 22.5 gal of water in 12 hr. How many liters can they…

A: Given that Camels have been reported to drink as much as 22.5 gal ofwater in 12 hr. Our Aim is to…

Q: Find the amplitude, the period in degrees, the phase shift in degrees, and the vertical shift. The…

A: A detailed solution is given below.

Q: Find the inverse transform of the given function of s. F (s) = A B C D E 6s - 49 s2-8s +41 f f (t)…

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Q: Consider the following. quadratic X y -2 5 -1 -3.5 0 -8 1 -8.5 2 -5 3 4 14 Find the equation of the…

A: The given data is:

Q: How do you evaluate the indefinite integral of 8sec(x)tan(x) ?

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Q: Use the washer method to find the volume of the solid generated by revolving the shaded region about…

A: Given curves y=1 ,y=cosx ,-π3≤x≤π3

Q: nd the center of the mass of a thin plate of constant density 8 covering the π gion bounded by the…

A: Please see the below picture for detailed solution.

Q: The function h(x) defined as: = 1 x+7 can be expressed in the form f(g(x)) where g(x) = (x + 7) and…

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Q: The base of a solid is the region bounded by the parabolas y = x² and y = 2 = x² . The…

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Q: x Inx - y Iny

A: Given fx,y=xlnx-ylny

Q: Two magnolia trees are 200 feet apart. From the point on the ground halfway between the trees the…

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Q: An oil retinery produces oil at a variable rate given by the following equation, where t is measured…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: 5.⁰0⁰ To determine whether the integral is divergent or convergent, do the following: 5e-da. Note…

A: a) find the value of ∫0b5e-xdx∫0b5e-xdx = ?

Q: he table shows the national expenditures for health care in the United States for selected years,…

A: a The table shows the national expenditure for healthcare. Let x be the number of years past 1950.…

Q: Evaluate the limit using the appropriate properties of limits. (If the limit is infinite, enter '∞'…

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Q: (siny-2ye¯*sinx) dx + (cosy + 2e-*cosx) dy = = 0

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Q: 10.88 The energy expenditure (in kcal/km) for animals swimming at the surface of the water is given…

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Q: Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the…

A: A detailed solution is given below.

Q: Find each x-value at which fis discontinuous and for each x-value, determine whether f is continuous…

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Q: 5. Using limits, find an equation of the line tangent to the function f(x) = 5x - 3x² at x = 2.

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Q: a) Graph the function f(x)=2x² + 4x b) Draw the tangent lines to the graphi t the points whose…

A: Note: As per our guidelines we are supposed to answer only three subparts if there are multiple…

Q: The amount in grams of a drug in the body t hours after taking a pill is given by A(t) = 30(0.85).…

A: Given The amount in grams of a drug in the body t hours after taking a pill is given by A( t ) = 30(…

Q: Let f(w) be a function of vector w, i.e. f(w) = 1+em³s 1+e-w²x Determine the first derivative and…

A: Given :fw=11+e-wTx

Q: Estimate using the linear approximation equation the value of 2023.

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Q: Which of the following functions satisfy the given differential equation? y" + 2y' =-y (a) ex D (b)…

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Q: Find the volume of the solid generated in the following situation. The region R bounded by the…

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Q: Find the inverse Laplace transform L-¹{F(s)} of the given function. 12s² - 21s +54 s(s² +9) Your…

A: Given function:- Fs=12s2-21s+54ss2+9

Q: The equation r(t) = (2 sin t) i + (5 cos t)j + (2t) k is the position of a particle in space at time…

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Q: 4: (1 zero? s) In what directions is the derivative of f(x,y) = (x-y)/(x² + y²) at P(1, 1) equal to

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Q: a) A pyramid has a height of 510 ft and its base covers an area of 15.0 acres (see figure below).…

A: (a) A pyramid has a height of 510 ft and its base covers an area of 15.0 acres.  The volume of a…