If f(x) = x2 + x and g(x) = x − 8, find f(g(x)) and g(f(x)). f(g(x)) = g(f(x)) =

Q: Evaluate the iterated integral by converting to polar coordinates. (x² + y?)3/2 dy dx dr de = Jo

A: Follow the procedure given below.

Q: The following figure shows the graphs of y = f(æ) and y = g(x), together with the %3D indicated…

A: Given problem:-

Q: За - 2 lim x3 - 1 O 2 O does not exist 13 8.

A: lim      (3x-2)/(x3 -1) x -- ∞ here ∞/∞ form so we use la hospital rule we differentiate above and…

Q: [-7, 1] The average value of cos (2z)e1-sin(2z) on is

A: The average value of the function f(z) on the interval a, b is  1b-a∫abf(z) dz.

Q: Are the following convergent or divergent? Show your work and state the reason 100 11) Ση n=0

A: The summation of n, n from 0 to 100.

Q: Let y=A cos x + B sinx is the solution of the differential equation

A:

Q: t sin(t² + 4) dt cos(t² + 4)

A: To evaluate: ∫tsint2+4cost2+4dt Let I = ∫tsint2+4cost2+4dt

Q: Consider the planes x – 10y – 2z = 3 and 2x – y + z = -13. Find the following. 1. A vector…

A: The given planes are: x-10y-2z=3 and 2x-y+z=-13 Let us assume z=t on the line of intersection, where…

Q: x4 - 4x3 + 4x2 + 1 2. Determine the open intervals where the graph of f(x) is concave upward or…

A: We can solve this as follows:

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Find y' (-1) if y = In (a² + 5)° (2 – 4æ)®

A: I have stated the used formulas in the solution

Q: Find the points on the curve where the tangent is horizontal or vertical. x = (t^3) − 3t, y = (t^2)…

A: Given

Q: A farmer has 1200 meters of fence and wants to construct a rectangular pasture. The pasture will be…

A: Explanation of the answer is as follows

Q: The domain of y = arcsinx is: -13x<1 all reals O-I to !

A: I am attaching image so that you understand each and every step.

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: x-axis from x = 0 to x = 6

A:

Q: Question 8 The magnitude, M, of an earthquake is measured using the Richter scale. The scale uses a…

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Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: F0 (-1)" Ln=1 By the 5n+1 series test:

A:

Q: Find the sum of the series 18 54 2+ 5 +... (if it exists). If the sum 125 - 25 does not exist,…

A: I am attaching image so that you understand each and every step.

Q: Show that la 1 1 1 a 1 - (а + 3)(а - 1)3. - 1)³. %3D 1 1 a 1 1 1 a

A:

Q: a L. determine whether the series Use the Integral Test to 2 Σ n=1 (2n – 1)4 is convergent or…

A: Solving

Q: An integral is given that can be evaluated using integration by parts. Write expressions for u, du,…

A:

Q: A spring has a normal length of 10 inches. It has also been determined that its spring constant is…

A: Given that a spring has a normal length of 10 inches. It has also been determined that its spring…

Q: Find the equation of the line tangent to Y = 3x² +x + 1 at = -3 %3D %3D O y = -17x - 26 o y = 6x – 3…

A:

Q: 3. In the differential equation (2x+ ydx-3(2x + y+4)dy =0, we let the substitution dy :

A: We can solve the given differential equation  by  using  the substitution            u = 2x+y

Q: Q1/ a) Sketch the graph of y = sin2x for 0 <x SI %3D b) find the total area bounded by the curve and…

A: This is a problem related to calculating area under curve of the polar equation. Based on the…

Q: Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

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Q: Find the solutions of the system of inequalities by graphing: x + y 2

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Q: Graph the curves and show that the 2x2-y2=C is a solution to yy'-2x=0.

A:

Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

A: Follow the procedure given below.

Q: d Calculate ri(t)· r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly and…

A: r1(t) =9t i + 2t2 j + 6t3 kdr1dt=9 i + 4t j + 18t2 kr2(t)=t4 kdr2dt=4t3 k

Q: 1. Determine the following using the graph of f provided below. If the value is infinite, specify ∞…

A: Solution: Given graph:

Q: Solve the problem. Given the velocity and initial position of a body moving along a coordinate line…

A: We can solve the given problem as follows:

Q: Find the Cartesian coordinates of the point (−√2,(5π)/4)

A:

Q: Find the solutions of the system of inequalities by graphing: 2x – y 0

A:

Q: iut n=1 Find the radius R of convergence for the series

A: Just use the formula of Radius of convergence and find it. Radius of Convergences, R= 1

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A:

Q: Let y = tan(4æ + 5). Find the differential dy when a = 5 and da 0.2 %3D %3D

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: 1. f(x)= Jx + 8x– 24 |

A: As per Bartleby guideline, only the first question has been answered.  Please repost mentioning the…

Q: Jse Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A:

Q: Suppose that a population of insects for an experiment increases according to the law of exponential…

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Q: An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per…

A:

Q: Knowing that harmonic series is divergent, which of the following series is also divergent by Limit…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A:

Q: If f(x) and g(x) are two functions defined on an interval then, ꭍ{f(x)±g(x)} is equal to? a.…

A: We have to choose correct option.

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by y…

A:

Q: Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x-y+z=2 and…

A: General equation of plane is taken and given planes are used.

Q: Compute f′(x). a) f(x) = (x2 +1) e−x^2  b) f(x) = (4e−x − e−3x)3  c) f (x) = x2 ln (x2 − 4) d) f…

A: Product Rule of differentiation : du.vdx = u.dvdx +dudx.v dxndx=n.xn-1 deaxdx=aeax Note : As per…

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: Given : r(t) =36-t2i + t2j-2tk   To Find : Domain

Q: Q2/ Find S*(4 – 3x) sinx dx -

A: Given: I=∫0π/44-3xsinxdx   As we know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx And…