of Find of and for the following function. ду 1(x,y) = (2x – 9y)5 %3D of 1 дх of 1 dy

Q: Which of the following functions grow faster than In x as x→ oo? Which grow at the same rate as In…

A: fx=lnx c. gx=1x Now, limx→∞gxfx=limx→∞1xlnx=limx→∞1x lnx=0 Hence fx=lnx and gx=1x grows at same…

Q: Calculate L6 for f(x) = v9x + 1 over [1,3]. (Give your answer to three decimal places.)

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Q: Evaluate the derivative of the given function for the given value of x. y = 8x + 8 , x= 8 OA. V72…

A: Given function is Differentiating with respect to x by using chain rule of differentiation, we get…

Q: For the given pair of functions, write the composite function and its derivative in terms of one…

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Q: Consider the following function. f(x) = x3/2 Find its average rate of change over the interval [4,…

A: Given function isAverage rate of change is given by the formula: When x = 4, the value of y is given…

Q: Suppose that the satifaction received from a number of rides taken on a roller coaster 2x+1\0.5 is…

A: The derivative of the ratio f(x)=u/v is given by,

Q: find the indicated derivatives. dz/dwif z = 1√w2 - 1

A: We need to find the derivative of the given z-function

Q: Given that the height of the cylinder is 6 cm and is growing at a rate of 5 cm/s, while the radius…

A:

Q: The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following…

A: Integrate marginal revenue and get total revenue

Q: 3. For which function is the average rate of change over the interval 1 < x < 5 greater than the…

A: To find- For which function is the average rate of change over the interval 1 &lt; x &lt; 5 greater…

Q: Suppose that the satisfaction received from a number of rides taken on a roller coaster is given by…

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Q: (d) Suppose that the satifaction received from a number of rides taken on a roller coaster is given…

A: To find the rate at which the satisfaction changes with respect to the number of rides taken, is…

Q: Find the linearizationsof the following functions at x = 0. ex

A: fx=ex at x=0. Now differentiating with respect to x, we get f/x=dexdx=ex Now, f0=e0=1 &amp; f/0=e0=1

Q: 4. Which of the following functions grows at the same rate as 3^ as x g O 2x O√√3x +4 3* O √6x 0x +…

A: To compare the rate of growth between the given functions lets draw their graphs. Given function 3x,…

Q: 3. Which of the following functions grow faster than x as x –→∞? Which grow at the same rate as x2?…

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Q: Given the function h(x) = x² + 6x + 5, determine the average rate of change of the function over the…

A: The average rate of change of the function f(x) is given by the formula f(b)-f(a)b-a. Here, the…

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given functions are: y=a2-t2x=42t2+a In order to calculate d2ydx2, firstly we will calculate d2ydt2…

Q: Calculate L6 for f(x) = v7x + 2 over [1,3]. (Give your answer to three decimal places.)

A: The given function is fx=7x+2 and the interval is 1,3. Obtain the length of the rectangle as…

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

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Q: d) Suppose that the satisfaction received from a number of rides taken on a roller coasteris given…

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Q: For the pair of functions, find the derivative of the composite function k(t(x)) in terms of one…

A: Obtain the composite function as,

Q: If x=t^2 +1 and y= t^3, then the second derivative is * 3 (4t)

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Q: Q1. Integrate the following functions with respect to x: y = 3x2 (1+x³)*

A: Explanation of the answer is as follows

Q: S Зх-7 dx 10х2+3x+11

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Q: Help

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Q: For the given pair of functions, write the composite function and its derivative in terms of one…

A:

Q: (d) Suppose that the satifaction received from a number of rides taken on a roller coaster 0.5…

A:

Q: The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following…

A: Given R'x=4xx2+25000-23

Q: Suppose that the satifaction received from a number of rides taken on a roller coaster         is…

A:

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Calculate L6 for f(x) = V9x + 3 over [1,3]. (Give your answer to three decimal places.)

A: Find the approximation L6 for the function fx=9x+3 over [1,3].

Q: Calculate L6 for f(x) = v5x + 3 over [1,3]. (Give your answer to three decimal places.) L6 =

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Q: Find the first and second derivatives of the functions s = t2 + 5t - 1/t2

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Q: Calculate L6 for f(x) = V6x + 2 over [1,3]. (Give your answer to three decimal places.) L6 2

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Q: Use the Product Rule to calculate the derivative for the function h(s) = (s¬12 + 4s) (1 – s-') at s…

A: d/dx (u.v)= UV'+VU'

Q: For the pair of functions, find the derivative of the composite function k(t(x)) in terms of one…

A: Consider the given pair of functions k(t) = 4.8t3 – 12t2 + 10t – 11;  t(x) = ln x

Q: Find the differential of the function  p = 5q − 6q3/2

A:

Q: Given the function h(x)=−x2−9x+26h(x)=−x2−9x+26, determine the average rate of change of the…

A: Given: The function is  h(x)=-x2-9x+26,     -6≤x≤-1   To determine: The average rate of change of…

Q: nd the derivative of the functionf(x) = v 5x+6 using the limiting proces A) S'x)= - 2 5x+6 Sx) = 2…

A: We are asked to find the derivatives of the function using limiting process.

Q: Determine if the following functions grow faster, slower, or at the same rate as the function 4x as…

A: Given a function f(x)= 4x^2  Part a) To find the function grow faster slower or at the same rate as…

Q: 3. Find the derivative of the following functions using the increment method. (10 pts each) 6- 3x 1…

A: a f(x) = 1/2-x now using increment method f'(x) = limh→0 [f(x+h) - f(x)]/h f'(x) =limh→0 [1/ 2-(x+h)…

Q: Find the derivative. y= e at O 4(1/4)x -4(5/4)x In 4 4(3/4)x In 4 4(5/4)x 25 n4 16

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Q: Calculate the average rate of change of the given function over the interval [4, 6] f(x) = 2x^2 + 7

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Q: find the absoute extrema for the function 5 (x )=9rX - 3x"on the given in tervalOL x < H

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Q: Given the function f(x) = 4x/3, which of the following is a valid formula for the instantaneous rate…

A: The objective is to find a valid formula for the instantaneous rate of change at x=27.

Q: Find the particular antiderivative of the following derivative that satisfies the C'(x) = 5x2 – 6x;…

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Q: (d) Suppose that the satifaction received from a number of rides taken on a roller coaster (2x+1°…

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Q: Find the derivative of the given function. 5x y= In 6+x dy xp %3D

A: SOLUTION-

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.