Part 1 1) Differentiate the following expressions (i) 5x2sinx (ii) 40 sin(20) 2e

Q: 1 ~ [ { f(x) dx = Given 0 (a) [f -11 f(x) dx = 0 and (b) for 22 (c) 0 f(x) dx. f(x) dx 1 [³ 3f(x)…

A: Due to Bartleby guidelines, only 3 sub parts can be solved. Please repost the remaining questions to…

Q: Consider the graph of the function g(x): 4 2 (C) 0 6 (D) ["g(z) g(x) dx = y = g(x) The graph from x…

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Q: Find the directional derivative of the function f(x, y, z) the vector v= (1, -2, 2). Answer: Dv f(0,…

A: Given f( x,y,z ) = xey + yez + zexGiven vector  { 1 , -2 , 2 }

Q: List the first five terms of the sequence. an = n3 – 7 а1 а2 аз О t a5 = || = || || ||

A: To find the first five terms of the given sequence

Q: 1. Rachel and Olivia work at a commercial greenhouse. It takes Rachel three times as long as Olivia…

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Q: If the figure below is the graph of the derivative f', answer the following: Where do the points of…

A: Given graph of f'

Q: 7000 is invested in a bank with an interest rate of 6 percent a year how much after 7 years if…

A: Given that Amount invested is 7000 and rate of interest is 6%.

Q: sinking fund is established to discharge a debt of $40,000 in 5 years. If deposits are made at the…

A: Given query is to find the amount of each payment.

Q: Compute the given indefinite integral. [(x − 2)(x) dx = - +C

A: Important formula÷ ∫xndx=xn+1n+1+C Let I= ∫x-2xdx Now we need to first multiply this expression

Q: increasing/decreasing

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Q: 6) Find the area of the part of the sphere X² + y² + Z² = 4 that lies within the cylinder X² + y² =…

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Q: the tangent line to the graph of the equation x + y − e^(x− y) = 9 at the point (5, 5). y =

A: the equation of tangent line is y=5

Q: (x, y) =(4, 2 Step 5 1/2+² To find the zeros, or x-intercepts of the function, we solve the equation…

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Q: Find all possible functions with the given derivative. t f'(t)=sin 2t- cos

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Q: Find the length of the arc of y^3= 8x^2 from x = 1 to x = 4.

A: Find the length of the arc of y^3= 8x^2  from x = 1 to x = 4

Q: 3 Consider the function ƒ(x) = 5x³ + 4zº – 10z³ An antiderivative of f(z) is F(x) = Aï” + Bx™ + Cr²…

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Q: Convert to a logarithmic equation. Gf=A

A: lnxn=nlnxlnab=lna-lnbgiven  Gf=A

Q: Let ƒ(x) = x³ – 15x² +27x - 2. Find the open intervals on which f is increasing (decreasing). Then…

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Q: and the length of the curve. y = x 2 + 1 10x³ 2≤x≤4

A: We know that length of curve is given by A=∫ab1+dydx2

Q: The profit function for a firm making widgets is P(x) = 154x - x² - 1600. Find the number of units…

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Q: (b) The Cartesian coordinates of a point are (2√/3, -2). (i) Find polar coordinates (r, 0) of the…

A: We need to change Cartesian to Polar.

Q: If a company has total costs C(x) = 10,000+ 15x + 0.2x² and total revenues given by R(x) = 265x…

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Q: Differentiate each function below. Be sure to use proper notation to distinguish between function…

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Q: _ƒ(x) = 2 sin X at x = 0.

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Q: Find the general solution to the given differential equation. (Remember the constant of…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √√1+3x,…

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Q: Evaluate dy and Ay for the function below at the indicated values. y=f(x) = 75 (1-2); x = 5, dx= x=…

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Q: Use the Mean Value Theorem and find all points 0<c<2 such that ƒ(2)-f(0) = f'(c) (2-0): f(x)=sin(x).

A: The given function is  f(x)=sinπx,  0&lt;c&lt;2

Q: Find f such that f'(x)=x² +4 and f(0) = 1. f(x) =

A: NOTE: Refresh your page if you can't see any equations. . take integration on both sides

Q: Find the integral. dx dx = - 2 +C ***

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Q: Cost, revenue, and profit are in dollars and x is the number of units. The average cost of a product…

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Q: Find the following. [(25 + y²) dx = [(x² + y²) dy =

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Q: mpute the directional derivative of the following function at the given point P in the direction of…

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Q: Water is flowing into a conical vessel 9 m deep and having a radius of 3 m across the top. If the…

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Q: 1. In economics, a Cobb-Douglas production function takes the form Y = AL³ Kº, where Y the output of…

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Q: Use the Integral Test to determine the convergence or divergence of the series. 2 Σn=15m+7

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Q: write the cubic polynomial function f(x) in expanded form with zeros -4, -1, and 3, given that…

A: given zeros  -4,-1 and 3standerd form is  f(x)=a(x+4)(x+1)(x-3)given   f(2)=20

Q: Out of all the techniques of integration (by parts, partial fractions, trigonometric) which one do…

A: Use the basic principle of integration by parts.

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. (-1)^…

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Q: 1 b (c) (-1)² (shape + (-1) + (x-1)²)

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Q: (a) What is the difference between a sequence and a series? A sequence is an ordered list of numbers…

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Q: A function f(x) and interval [a,b] are given. Check if the Mean Value Theorem can be applied to f on…

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Q: The figure above shows the graph of the continuous function f. The regions A, B, C, D, and E have…

A: The area of region A =5It is above x - axis therefore, ∫-7-5f(t)dt = 5The area of region B =2That is…

Q: a. Evaluate b. Evaluate X √√x+2 X dx using integration by parts. dx using substitution. √√x+2 c.…

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Q: After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world…

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Q: Compute the coefficients for the Taylor series for the following function about the given point and…

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Q: Let u(x) = f(x)g(x) and v(x) (a) Find u'(1). (b) Find v'(5). = f(x) g(x)

A: Given that: ux=fxgxand vx=fxgxThe Blue line represents the graph of fx and green line represents the…

Q: a. Find the linear approximation for the following function at the given point. b. Use part (a) to…

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Q: Given z = = f(x,y), x= x(u, v), y = y(u, v), with x(3, 3) = 5 and y(3, 3) = 4, calculate zu(3, 3) in…

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Q: (a) The Cartesian coordinates of a point are (1, 1). (i) Find polar coordinates (r, 0) of the point,…

A: we need to find the polar coordinates