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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:...

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Q: Replace the Cartesian equation with equivalentpolar equations. x2/9 + y2/4 = 1

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Q: Find F'(x) if F(x) = Vidt 3

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Q: In 2007, world population was approximately 6.6 x 109.By some projections, world population will dou...

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Q: calculate the length of the curve, L.

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Q: Find the most general antiderivative of the function.(Check your answer by differentiation.) f ( x...

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Q: For which positive numbers a is it true that a" > 1 + x for all x?

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Q: Consider the point (x, y) lying on the graph of the line 2x + 4y = 5. Let L be the distance from the...

A: To write the distance L as a function of x.

Q: Find the volume of the solid that is bounded above by the cylinder z = x2 and below by the region en...

A: Given Data The equation of the cylinder is z=x². The equation of parabola is y=2-x². The equation of...

Q: A puppy weighs 0.85 lb at birth, and each week he gains 26% in weight. Let an be his weight in pound...

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Q: Consider the function. ={-2 if z>1 if x 1 Then f(0) = f(2) = 0. Your friend claims that by the Mean ...

A: Given function is,

Q: Calculus Question

A: Given a=1.41 , b=2.01 , C=51.9 degree

Q: Let f (x) =2x³ + 2x² + 3x – 2. Use the mean value theorem to find the set of x values in the interva...

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Q: Suppose, f'(x)= 2 cos x+sec x, -7<x<, and it is known that and it is known that f()=4. Find the func...

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Q: Given the linear approximation at a=0, determine the smallest value x of such that the linear approx...

A: the linear approximation of f(x) at a is : ...

Q: Q(x, y) = 42x1/5,A15 Where Q is the output in millions of units of product.

A: Given data: The given output of the factory is: Q(x,y)=42x1/5y4/5. The sum of the amount spent o...

Q: In the year 1980, the city of Gumbolantenden had a population of 20,000. The population of Gumbolant...

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Q: 16-x dx

A: Given data: The given integral is: Assume x=4sint and differentiate it with respect to t. The ...

Q: An arithmetic sequence begins 2, 6, 10, 14, 18, . ... (a) Find the common difference d for this sequ...

A: Given arithmetic sequence is

Q: Find the global maximum and minimum of the function on the given interval:f(x)=x+2/x,x∈[0.5,2].

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Q: Find all values of in the interval 0, 2 such that sin x = sin 2x

A: To find all values in the interval for the function

Q: Determine whether the series ∞∑n=1 / 11+10n converges or diverges.

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Q: he cost of producing x smart phones is C(x) = x2 + 400x + 4000. (a) Use C(x) to find the avera...

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Q: Represent 1/7 and 4/27 as infinite repeating decimals.

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Q: A sequence is defined recursively by an +1 = 3a, - n, a1 = 2. Find the first six terms of the sequen...

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Q: Evaluate the definite integral. •3 3x Vx3 + 1 dx

A: Given the definite integral is

Q: World Population The total world population is forecast to be P(t) = 0.00075t3 − 0.0716t2 + 0.99t +...

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Q: Find 10 partial sums of the series. (Round your answers to five decimal places 15 (-4)" n = 1 Sn 1 -...

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Q: evaluate the integral.

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Q: Given: g(x,v,=) =x'In (xy+ =) Find the direction of maximum ascent at (2,1,3).

A: Given Data The function is g(x,y,z)=x²ln(xy+z). The point is (2,1,3). Differentiate the function w...

Q: Factor and simplify algebraic expression.

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Q: 5. Let a curve be parameterized by x = t³ + 9t, y =t+3 for 1 <t < 2. Set up and evaluate the integra...

A: A curve is parameterized by for .

Q: Evaluate the line integral ∫Cx2yds along the segment of the line y=x from the origin up to the point...

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Q: The population P (in thousands) of a country can be modeled by P = -14.73t2+788.5t +117212 Determ...

A: Given Data The equation of the population of a country is P=-14.37t²+788.5t+117212. Differentiate ...

Q: Scalar line integrals Evaluate the following line integral along the curve C.

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Q: on the interval [4,16]

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Q: Find an equation for the ellipse with center (2, 0), foci (2, ±3) and major axis of length 8.

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