Find the arc length L of the graph of r(t). 1 r(t) = t³ i + t j + = √√61² k, L = i I 2≤1≤7

Q: 4) A company purchases a new machine for which the rate of depreciation is dv maner 10,000(t-6),0 ≤…

A: Given query is to find the total loass of the value in first 3 years.

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Q: 1. If g (2) = 59 and fg'(x) dx = 25, what is g(5)?

A: Since you have posted a multiple question, we will solve the first question for you. If you want any…

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Q: QUESTION 13 Given the following inequalities, fill in the blanks to list the corner points in order…

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A: Given the query is to find which graph is  function and which one is derivative.

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Q: Express the limit as a definite integral on the given interval. n exi lim -Ax [0, 9] n→∞ i = 1 6 +…

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Q: For f(x) = 2x³ - 2, find ƒ '(x) using the definition f '(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using…

A: Let's find.

Q: (y² +1)dx +(2xy+1)dy

A: (y2+1)dx+(2xy+1)dy=0  It is of the form Mdx+Ndy=0whereM=y2+1N=2xy+1Then ∂M∂y=2y       ∂N∂x=2ysince…

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Q: The Bernoulli's form of the differential equation 2x³dy-− y(y² + 3x² ]dx = 0 is

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: Find the exact value of the logarithmic expression without using a calculator. (If not possible,…

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Q: Use the figure below to find the exact value of the trigonometric function of angle A. csc (A)

A: answer is in next step

Q: 1) Use the definition of the derivative (which involves limits) to calculate g'(x) if g(x) = 3x² 5.…

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Q: Change from rectangular to cylindrical coordinates. (a) (3, 3, 4) (r, 0, z) =

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: For a certain model of car the distance of required to stop the vehicle if it is traveling at v milh…

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Q: 2) Find the relative maximum or minimum value of f(x, y) = 3x² + 2xy + 10y² - 54x - 308y

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Q: Factor and find the zeros of the following polynomial and write its behavior.

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Q: Compute the flux of the vector field F = 2xi + 2yj through the surface S, which is the part of the…

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Q: xdy-[y+xy' (1+ In x)]dx=0 is

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Q: c) y = x(x + 2)(x-1)² y

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Q: 3x hp Find for 2 Әх (2x + 3y) 5. Select the correct answer below: 15(2x + 3y) O 10(2x + 3y)4 О Зу 2x…

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Q: 12. If f(x, y) = √√4 – x² – 4y², find fx(1, 0) and f(1, 0) and interpret these numbers as slopes.…

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Q: 1. Let Evaluate the following limit. 7 (t) = (t² + 5, t²-5t+6 t²-9 lim r(t). t-3 > sin(πt)).

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Q: Using trigonometric substitution to evaluate: The first thing we'll need to do here is complete the…

A: Here, we just need the complete square for the factor in the denominator (40-6z-z2)

Q: 4. Find the absolute extrema of the function f(x, y) = ry-x-3y on the triangular region with…

A: To find the absolute extrema of the function f(x,y).

Q: Use the properties of logarithms to write the logarithm in terms of log3 (2) and log (5) log 3 (10)

A: Note that: log (a×b)=log a+log b

Q: For f(x) = √x+1, find ƒ'(x) using the definition f'(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using this,…

A: TOPIC -derivative using limits and equation of tangent line

Q: Consider the following function. f(x) = (8 - x)(x + 1)² (a) Find the critical numbers of f. (Enter…

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Q: STU વપ (y-1) Ty

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Q: 3 4d³y - 13d +6y=0 dy dx3 dx

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Q: x² x-o ex-x-1 Evaluate lim А A) 0 B) 1 C) 2 D ∞ by applying L'Hôpital's rule.

A: find limit using L hospital rule option C correct answer

Q: Find for z = for z = ex-y Əz Əx

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Q: Use synthetic division to find the quotient and the remainder. (3x4 -8x3+8x-5)÷(x-2) (3x4…

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Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j; t = T(-₁) = (53) 3. N(₁) = Z =…

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Q: An angle's initial ray points in the 3-o'clock direction and the angle measures radians. Which of…

A: We have to choose correct option

Q: A point starts at (x, y) (5,0) and moves CCW along a circular path that is centered at (x, y) (0,…

A: A point starts at x, y=5, 0 and moves CCW along a circular path that is centered at x, y=0, 0.…

Q: Water is flowing into a tank at a rate of r(t) = 3√2 cubic meters per minute. How much water entered…

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Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A: The Maclaurin series for f(x) is given by f(x) = f(0) + f'(0)1!x + f''(0)2!x2 + f'''(0)3!x3 + …

Q: A circle is centered at an angle's vertex. The angle's rays subtend an arc that is 6.6 cm long, and…

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Q: A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a rate…

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Q: A hive of bees contains 27 bees when it is first discovered. After 3 days, there are 36 bees. It is…

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Q: The total profit P(x) (in thousands of dollars) from the sale of x hundred thousand automobile tires…

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Q: From November to December of 2015, the price per share of BP Oil dropped from $95.25 to $62.25.…

A: We can solve as follows

Q: The heights on the graph of f'(x) correspond to the slopes of the lines tangent to the graph of f.…

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Q: Given the graph of f, determine which is larger in each case. 10 f(6) is [Select] than f(8)…

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Q: ∫x2(x3-1)11dx

A: Given, ∫x2(x3-1)11dx We can solve it by substitution method

Q: Compute the flux of the vector field F(x, y, z) = 3x + 3yk through the surface S, where S is the…

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Q: A beauty supply store expects to sell 120 flat irons during the next year. It costs $4.80 to store…

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