Find the volume of the solid that results when the region enclosed by 4x 0, x = 1, and y = 0 is revolved about the x-axis. 6. V1 + e8x*

Q: Find the most general antiderivative or indefinite integral. Use a capital letter C to ote an…

A: ∫ -2x1-x2dx

Q: Evaluat each Integral. For definite integrals, give exact valaes Only, rF - 7+" -ム dt

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Q: 2. Find the directional derivative of o = yx2 +x²z + 3xyz in the direction of vector n = î + 2 ŷ -2·

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Q: 9. Set up the integral to calculate the area between the curves f(x)=x* – 2x g(x)=-2x+1 A. g(x)-…

A: To set up the integral to calculate the area between the curves.

Q: For the function f, use composition of functions to show that f 1 is as given. 7x -7 f(x) = =x+1, f…

A:

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Q: For what Valuer of the Constant(k that the function fayt=x"+kxy+y will have a- Saddte Point b-local…

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Q: Find the radius of convergence, R, of the series. (x + 5)" 5n In(n) n = 2 R = 5 Find the interval,…

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Q: Find the average value of the function J (1) = VI +1 from x =0 to x = 3.

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Q: Graph the function and its inverse using a graphing calculator. Use an inverse graphing feature, if…

A: To solve the following problem

Q: dx Vx2 + 2

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Q: S 2x(x² – 2x)dx

A: Solving the problem by finding the value of the integration.

Q: If Rita receives $39.24 interest for a deposit earning 6% simple interest for 110 days, what is the…

A: This is a problem related to simple interest. Based on the general formula of simple interest we…

Q: Find the equation of the tangent line at the given point on the curve. 3y-Vx = 8, (16,2) y =

A:

Q: Use the Laplace transform to solve the following initial value problem: y" + 4y/ + 29y = d(t – 5)…

A: Taking Laplace transform on both sides and solve it.

Q: 3) Derivative Applications a) A particle moves according to the function f (t) = -9t2 + 15t, t 2 0,…

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Q: Given the function f(x) =

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Q: Evaluate the integral using integration by parts. cos

A: We can solve as follows

Q: For numbers 17- 20, use the given function. (5 + 2x, x <- 6 f(x) = } x +5, x 2- 6 17. What is the…

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Q: Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 2 y + 5 = z +…

A: Given that equation of line x-28=y+57=z+71Solution :x-28=y+57=z+71=tx=8t+2y=7t-5z=t-7point…

Q: -............... ...................... ..…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Use the Ratio Test to determine the radius of convergence of x" Σ Vn : 11" n=1 Then determine…

A: Let's find.

Q: Find the derivative of the function y = (tan '(z) ). ช่ ||

A: To find the derivative of  y=(tan-1(x))23

Q: Y = 1 - x², y = 2 + 2x, and y = 2– 2x

A: Let's find.

Q: find the domain of the following equation: f(x) = 4 Vx2 – 4

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Q: ;Which sequence is increasing ? 7n-21 4n -7n+2 4n 4n+2 7n 7(-1)" 4 None of the others

A: We need to determine which sequence is increasing.

Q: х—1 dx c4 –1

A: Basic integration is done.

Q: One face of the semicircular fin shown in the figure will be painted blue, with a circular hole…

A: Given:  A quarter circular fin with a circular hole. AB = 120cm.  Thickness of paint = 2mm  = 0.2cm…

Q: Question 14 (2) + h(x)]dr 8 1.5 -2/6 -7 -6 Blank 1:

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Q: 2. Find the dimensions of a rectangle with an area of 225 square cm, whose perimeter is as small as…

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Q: Consider the angle shown below that has a radian measure of 0. A circle with a radius of 3 cm is…

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Q: Integration by Trigonometric Subshtunon SxCx?- ax+4) $12 XP

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Q: The graph of the derivative f' of a function f is shown. y = f'(x) 2 4 6 (a) On what intervals is f…

A: Let's find.

Q: n 10 2x dx te the integral (x² + 1)3 (x? + 1)-3 +c

A: We  have to choose the correct option from the given options

Q: The integral gives the area of the region in the xy-plane. Sketch the region, label each bounding…

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Q: 3. a) Use the sum of the first 10 terms to estimate the sum of the given series. n-1 b) Improve this…

A: We have to find the sum and improve the estimates.

Q: 9! Calculate 7. 4! 5! 3024 15120 1814400 126

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Q: Find the dimensions of the rectangle with maximum area that can be in- scribed in the ellipse x2/a²…

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Q: 1. Determine if each series converges or diverges, you can use any of the tests discussed in class.…

A: a) ∑n=1∞3nen-1b) ∑n=1∞1+3n2nc) ∑n=3∞3n-14n

Q: Question 1 f(a)da 7 -2 3

A: The given figure is:

Q: Find the derivative of the function F(s) = In(9 ln(8s)). F'(s)

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Q: 253 4x

A: Given query is to find the value of the integral.

Q: Find the equation of the tangent line at the given point on the curve. 2x2 + 2y? 29y-y e 58x/5, .2…

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Q: х—1 dx х4—1

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Q: Given the area of the region enclosed by y = x and y = -2x* , identify the "a" and "b".

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Q: x2 dy dx2 d²y dy + 2y = 5x° cos(x) 2x Jx - dr solve the equation by undetermined coefficients method

A: