Evaluate the following improper integrals. Tell whether it is convergent or divergent. 1.

Q: a(2))® dz: Consider the indefinite integral This can be transformed into a basic integral by letting…

A: Consider the indefinite integral

Q: Solve the initial value problem. 4 y(x) = 4 sec(3.xr) tan(3x) ; y(7) = 3

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Q: Find the third degree Taylor polynomial centered at 2 for the function f(x)=e²* + 3.x .

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Q: Evaluate the definite integral. Write your answer in terms of . (y +1) dy

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Q: V19+r* dt , find f'(C

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Q: sin e = If and 0 in the first quadrant, find Cos 20

A: A detailed solution is given below.

Q: Use the summation properties and rules to evaluate the series. 5 E (312 - 21 + 6) i= 1 5 E (31? - 21…

A: Use the summation properties and rules to evaluate the series.

Q: 47. f(x) = V(3 – x) on [1,3]

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Q: 3. Find the equation of the plane tangent to xyz + x² – 2y² +z' =14 at (5,–2,3)

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Q: xp Evaluate the definite integral.

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Q: +2 dx: Consider the indefinite integral a) This can be transformed into a basic integral by letting…

A: The given integral,        ∫e7x+2dx

Q: 10 X=-3

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Q: Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the 74-kilometer mark…

A: Solution is done in step 2

Q: Question 6 Find the area, A, of the region enclosed by the cardioid r = 8 + 8 cos 0. 48 n 96 n 52 n…

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Q: Give the representation, equations and solution. Use elimination, comparison or substitution to…

A: Sum of two numbers =  25 Difference of two numbers = 7

Q: Evaluate the indefinite integral. (Use C for the constant of i | sec?(e) tan°(e) de

A: Topic:- integration

Q: ​(A) Find the average value of the function over the indicated interval.   ​(B) Graph the function…

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Q: Solve the following differential equations of e • dx+2(xe" – y)dy = 0;

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Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 81 – x…

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Q: Without graphing, find the horizontal and vertical asymptotes, if any, of the curves. Show your…

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Q: Q2) Apply the differentiation rules to find the derivatives of: Inx 5 (a) y=x*.e*+2- Inx- cosx (b)…

A: Solve the following

Q: ving limits. Since you

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Q: The derivative with respect to x of | (3Vi-1) dr is 3x – 1 by the 2nd fundamental theorem of…

A: Given that,         ∫3x3t-1dt

Q: Express the area of the region bounded by the given line and parabola as an iterated double…

A: The equation of the line and the parabola are: C1: y = x2…

Q: Question 14 Find the volume of the indicated region by an iterated integration. The region that lies…

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Q: dr

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Q: 2) Evaluate the integral S inx dr 2.

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Q: Evaluate the double integral. / 5x(4 + y) dA; R R is the region in the first quadrant enclosed by y…

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Q: Solve the initial value problem. 1 u'(x) = – 2; u(0) = 1 x2+1

A: Explanation of the answer is as follows

Q: Use Newton's method to approximate the indicated root of the equation correct to six decimal place…

A: Here, let the given function be: f(x)=x2+ex-9⇒f'(x)=2x+ex Next,…

Q: Evaluate the sum using the given information. X1 = - 3, X2 = - 1, and x3 = 2 Xj - 5 Σ 2x; + 4 3 j= 1…

A: Solution is given below:

Q: Question 5 Find the volume of the solid that results when the region enclosed by the given curves is…

A: To find the volume of the solid that results when the region enclosed by the given curves is…

Q: 13. 1²V2 - 1 dr

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

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Q: Verify the Divergence Theorem by evaluating F.N dS as a surface integral and as a triple integral.…

A: Here, using the Divergence Theorem, ∯F·Nds=∫∫∫v∇·Fdv Here, F=xy,z,x+y So, ∇·F=∂F∂x,∂F∂y,∂F∂z=y,0,0

Q: 6. Write an expression equal to log3(4) + log,(5) |using at most one log. 7. Give one example a that…

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Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Here,  0≤x≤4-yy≤z≤8-y0≤y≤4 To change the order of integration to dx dz dy to dz dy dx

Q: Convergent. or divergent dx ra5-x 3 25-X

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Q: 33) In Problems 33) through 35), given MB ' (x) = HD(x), HD' (x) = PR (x) , PR' (x) = RB(x) with the…

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Q: dr 2 Vr*+3

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Q: Question 5 3 Consider the function f(x) = Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

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Q: ph of the parabola to fill in the table. 10- (a) Does the parabola open upward or downward? O=0 6+…

A: Given query is to find characteristics of parabola.

Q: Differentiate. 9. y = e

A: As per the guidelines I am sharing the solution to the first question.

Q: Solve the initial value problem. x'(t) -x = 1; x(0) = 3

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Q: tó úsé co ór -0o, enter INFINITY or -INFINITY, respectively.) (-1)" + 1n! 1. 8. 15 ... (7n + 1) n =…

A: Solve the following

Q: Use series to evaluate lim 3x(e -2/x - 1). lim 3x (e -2/* - 1) -O X00 (Simplify your answer.)

A: We can use series to find the limit as below.

Q: (x) = V19+r dt , find f'(3)

A: Given query is to find indicated derivative.

Q: 19 Suppose that Ts (x) centered at 2 for f(x) is gien by. Is (X=3+5Cx-2)+8(x-2)²+2G-2)°+(x-2) (3)…

A: T5(x) centered at 2 for f(x) is given by,T5(x)=3+5(x-2)+8(x-2)2+2(x-2)3+(x-2)5

Q: C. coordinate

A: answer is in next step

Q: 2 - x 3. Let f(x) = ! + In x. It is known that f'(x) 1 and f"(x) = x2 x3 (a) State the domain of f.…

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