Find the average value of f(x) = 3 sin (x) + 5 cos (x) over the interval 0, [0]. 3

Q: Find the directional derivative Duf (2,0) where, f(x, y) = xexy + y and u is the unit vector in the…

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Q: Find the general antiderivative of f (x) = 4 x ln x²

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Q: Let D be the region enclosed by y = sin(x), y = cos(x), x = 0 and x = . revolving D about the x-axis…

A: Given problem:- Let D be the region enclosed by y = sin(x), y = cos(x), x = 0 and x = π/6 The volume…

Q: b) Use chain rule 1 y= LESANNE aretan u where u eª ue

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Q: The height y (in feet) of a ball thrown by a ch 1 -x² + 6x + 5 - y = 14 where is the horizontal…

A: The height of the ball is given by  y=-114x2+6x+5 in feet where x is horizontal distance from child.…

Q: dx (4+x²)² √

A: Explained below

Q: (2) Evaluate the iterated integral by converting to polar coordinates. 1 √x-x² (x² + y²) dx dy [] 0…

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Q: tid Q3. Evaluate the following integrals 1) cothx.csch2x. dx (50-3x - √x+1+73 44x

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Q: a Find the general flow pattern of the network shown in the figure. b. Assuming that the flow must…

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Q: P3: Calculate the volume of solid of revolution when the region bounded by y = sin 2x and x²-y-2 = 0…

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Q: Question R is the region bounded by the functions f(x) = 2-3 sin (x) and g(x) = 4 cos (x). Find the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: ● -5 13 10 5 Enable Zoom/Pan x -10 10 5 Keyboard cting a radio button will replace the entered…

A: We will solve the limit.

Q: cteria. If the bacteria grows continuously, how many will there be at 7:30 pm?

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Q: y = ln x and x - y -4 = 0

A: Explanation of the answer is as follows

Q: At 12:00 noon, there were 200 bacteria present. By 4:00 pm, there were 379 bacteria. If the bacteria…

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Q: Consider the second order differential equation with initial conditions u" - 4.5u' - 5.5u = -4…

A: The given equation is u" - 4.5u' - 5.5u = - 4sin(3t)

Q: Find the area that lies inside both curve: r = 1 – cos(θ) and r = 1 + cos(θ). Draw.

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Q: Power series p₁(x) and p2(x) are given below. P₁(x) = 1 + 7x +49x² + 343x³ +2401x² + ... P2(x) = 1 +…

A: Here, to find the series notations of p1(x)+p2(x)

Q: Use the following information to answer the next question the graph shown below is obtained by…

A: Please refer to the image below

Q: (a) Assume that f(x) is a function defined by f(x) = x²-3x+1 2x - 1 for 2 ≤ x ≤ 3. Prove that f(x)…

A: Given.

Q: . What is the snortest distance between the parabola y=2x² and the line y=4x-4

A: Shortest distance between two curves are always along the common normal.

Q: 3. Given f(x) = cot(x) sin(x) and g(x) = cos³(-x)(sec² (x)-1) sin² (x) a. Prove that f(x) = g(x).…

A: Given that,  fx=cotxsinx and gx=cos3-xsec2x-1sin2x

Q: The function of given by f(t) = 10e0.07t models the balance in a bank account, in thousands of…

A: Use exponential growth formula for finding the first two .

Q: Find the sum of the first eight terms of the sequence shown. 1/2, -1/4, 1/8 . . . a. 1/256 b. -1/256…

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Q: Find the area of M. == Let M be the region bounded by the parabola y (0,2) (-2,0) 4 0 L N ရာ T c…

A: Given problem:- Find M be the region bounded by the parabola y=(-1/2)x2+2 and the line y = - x - 2 .

Q: Question 13 Which of the following satisfies the differential equation d²y dx² A. y = e³r B.y = e-3r…

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Q: farm bureau Determine the open intervals on which the function is increasing, decreasing, or…

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Q: 4. Find the slope of the tangent to y = sin² (2x) at x = 12

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Q: Find ď²y dx² x = 3 sin t in the parametric equation y = 3 cost 0≤t≤ 2π.

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Q: 1. Find the value of (0) for a solution (x) to the initial value problem: 6y"+y' - 2y = 0; y(1) = 2,…

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Q: Differentiate and simplify this function g (y) = y3 / ln(2y)

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Q: b) Calculate (i) the following integrals x² (3x³ + 2)²dx

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Q: 10-x-x² if x 5 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) =…

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Q: 5. Find the limit, if it exists. If the limit does not exist, explain why. sin x - cos x (a) lim…

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Q: Homework Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule.…

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Q: The Kirk Kelly Kandy Company makes two kinds of candy, Kisses and Kreams. The profit, in dollars,…

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Q: Find the value for k so that the function will be continuous at x = -4. f(x) = 7x + 47 -x² + 18x81+k…

A: Topic = Functions

Q: Find the tangent line(s) to the parametric curve given by z = t¹ - 9t² and y = t² at (0, 9).

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Q: What is the average rate of change of f(x) from x₁ = -8.2 to x₂ = 2.8? Please write your answer…

A: Follow the procedure given below.

Q: 5. Estimate to 4th place accuracy, i.e. within 0.00005 of cos(2º) using its Mac- xpansion. Justify…

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Q: EXAMPLE 1(DISK METHOD) Find the volume of the solid generated by revolving about the x-axis,the…

A: Given problem:- EXAMPLE 1(DISK METHOD)   Find the volume of the solid generated by revolving about…

Q: Sv x² - 36 dx

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Q: Solve the equation using Exponential Shift (D² - 2D + 2) y = 12x³e²x O y = e (c! COSx + c2 sinx) +…

A: Answer is given.

Q: Which relation is incorrect: a. i.j = 0 d. j.k=i b. ixj=k e. ii 1 c. ixi=0

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Q: problem: Find the vector below. ting the unit normal vector of A = 40 + 7 ₁ 0 - 3 K

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, cos x = 0, y() = 0…

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Q: Evaluate the limits - im 1 lim x→-2 X

A: limit x→-2 1x3

Q: Find the area of the surface generated when the given curve is revolved about the x-axis. 3 X 1 1 /=…

A: Given problem:- Find the area of the surface generated when the given curve is revolved about the…

Q: Find the equation of the tangent line to the polar curve r = 2 – sin(θ) at θ = π/3. Draw

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Q: y 3. The region bounded by the curve y=sec x, the x axis, the axis and the line x=0.25pi is revolved…

A: The given curves are; y=secx, y=0 x-axis, x=0 y-axis, x=0.25π So, the bounded region is as shown…