7. Determine the volume of the region that lies under the sphere x² + y² +2²=9, above the plane z = 0 and inside the cylinder x² + y² = 5.

Q: Evaluate lim x-0 1-√√1+x X

A: Given problem:-

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A: Given:-Area of plates=0.45 m2distance between plate, d=1 cm=10-2mthickness of permittivity ,…

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A: Finding the derivative of the function.

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A:

Q: (CLO-2) Find the linear approximation, L(x), to f(x) at x = xo - f(x)=√√6x+64, x = 0 O L(x)=-x-3…

A: Given f(x)=√(-6x+64)  We hav eto find the linear approximation of f(x) at x=0.

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A: Equation of tangent to curve is given.

Q: Σ (-1)" n=0 2n TT (2n)!

A: Given: The series is  ∑n=0∞ (-1)n π2n(2n)!

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A:

Q: {CLO-3} The critical number(s), if any, of the function O -1. 12.2 01/14 2 O 0, 1, 2 O There is no…

A:

Q: Find the particular solution (D² + 4D + 4)y=0 when x = 0, y = 1 and y = -1 What is the particular…

A:

Q: Find the Laplace Transform

A: Topic:- application of integration

Q: What is the area of the region between X |y=x2–2x−3 and the x-axis from x=0 to x=4?

A:

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.

Q: At 12:00 noon, there were 225 bacteria present. By 4:00 pm, there were 427 bacteria. If the bacteria…

A:

Q: * Use Cramer's rule to solve the equation X +y +z 2x -y 3x +2y -z ↑ Add file || || || 1 4 -3

A:

Q: x-1 x-1+√√2x-x²-1 Evaluate lim

A: Please refer to the image below

Q: Jmin = ymax =

A:

Q: -1 position (s, cm) 153 10- 5+ 0 2 3 4 time (t, seconds) 5

A: Slope of position(s) graph gives speed. i.e. Speed =dsdt

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A:

Q: r sin ³0 cos³ 8 do 3

A: Topic:- application of integration and trigonometry

Q: 2. Evaluate: S 0 trư √2 = x + x dx

A:

Q: Evaluate the triple integral a dV where E is the solid bounded by the paraboloid a = 10y² + 102² and…

A:

Q: Q3/Find the value of xx If the approximation of the integral ff(x)dx by trapezoidal method is given…

A:

Q: S x²-x+1 x² + 2x + 2 2 -dx

A: We need to evaluate integral.

Q: A retailer has been selling 1,000 computers a week at $750 each. The marketing department predicts…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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A:

Q: Given: vector-valued function Ř(t) = (3 cos 2t, 9t, −3 sin 2t) 1. Reparametrize R using the directed…

A:

Q: y = 25

A: Topic:- function

Q: √√5³-25² 2s + s ds

A:

Q: 3. LL₁a+ (x + 2y) dy dx

A:

Q: (CLO-3) Find the absolute maximum value of the function f(x)=x³-12x+3 on the closed interval [-4,3].

A:

Q: Use linear approximation, i.e. the tangent line, to approximate √25.2 as follows: Let f(x)=√x. Find…

A: Linear approximation for fx=x at a=25The linear approximation of the function fx at point a is Lx =…

Q: The half life of a decaying substance is the amount of time it takes for the substance to reduced to…

A: Let us assume it takes n half-lifes to reach 10mg

Q: Find Vf at the given point. f(x,y,z) = x² + y² - 4z²+zlnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k…

A: Topic:- application of derivatives

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

A:

Q: Carbon extracted from an ancient skull combined only one-sixth as much as C14 as carbon extracted…

A: Let's find age of skull.

Q: Evaluate the following integrals: 0 (Cartesian to Polar) Given the cartesian coordinate, find FOUR…

A:

Q: Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 62² and…

A:

Q: 1. Find the general indefinite integral. 5e + 3 sin x dx (b) ["be²

A: We have to solve this given integral . For this first we solve the general indefinite integral &…

Q: (e²t-e-2¹) ² None of the choices Option 1 1 S 32 s(s² - 16) I Option 3 + 25 1 s+4 32 s(s² + 16)…

A:

Q: Consider the following series, (x - 2)" Σ n5 + 1 n=0 (a) Find the radius of convergence, R , of the…

A:

Q: If given f(3) = -1 and f'(3)=5, the tangent line to the graph y = f(x) at x=3 is y = 5x +16. (a)…

A: This question is based on finding tangent equation at a point on function.

Q: 6) Calculate - dx for z = ln(x + y²).

A:

Q: Evaluate the triple integral zdV, where E is bounded by the cylinder y² + 2² = 4 and the planes z =…

A: Given problem:- Evaluate the ∫∫∫E z dV, where E is bounded by the cylinder y2+z2=4 and the planes z…

Q: Given the rectangular coordinates (-6,2) determine (r,θ). What is r=______. (round to 1 decimal)

A: r is obtained.

Q: Use the Euler method to solve the following equation analytically for five iterations. Given that…

A:

Q: Find the value of the following mplicit derivative tan y-sec x=5 find...y'

A: Given query is to find the derivative of the expression.

Q: A horse tied to a post with twenty foot loop. What is the longest path that the horse can walk? a.…

A: Here we have to find the circumference of a circle.

Q: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high…

A:

Q: Use cylindricoll shells to find the volume shells of the solid obtained by rotating the region…

A: Given region is bounded by y=x2 , y=0 and x=6 rotating about y -axis