Express the limit lim E (4 cos (272;) + 6)A¤; [2, 4] over as an integral. n- 00 i=1

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

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Q: -3 2. (2x+4)3 8x dX use integration by parts and then find the value of definite integral.

A: A detailed solution is given below.

Q: 2. The sum of a two-digit number is 13. When 27 is added to the original number, the result is the…

A: To find out the original number.

Q: If y= In Cschx + coth y Biod dy

A: Given: y=lncschx+cothx

Q: Hi, I believe the function was not entered correctly in the transcription. It should be x^2-16/x-2.…

A: Apologies for the inconvenience. First two steps were correct in the original solution. Step 3 was…

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

A:

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

A: Topic:- integration

Q: Find V x (V × F) if F(x, y, z) = xyj+ 6xyz k. V × (V × F) =

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Q: dr 10. dr 11. (x – 1)2 12. sec 20 tan 20 de

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. V16–z? xy dy dx dz =

A: Application of integration

Q: Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

A: We have to find integral

Q: Use a triple integral to find the volume of the region bounded by z = 7x + 8y, z = 9, and the planes…

A: Let's find.

Q: x³ Jx² +3dx

A:

Q: A forest has a population of cougars and a population of rabbits. Let æ represent the number of…

A: A detailed 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: Given, y= sqrt(25-x²) y= 4

Q: The sum of the digits of a three-digit number is 11. The tens digit is three times the hundreds…

A: Let a be the hundreds digit, b be the tens digit and c be the units digit. Thus our required three…

Q: 2. If ā = 3i - 27 + ok and b =(4,-1,-6) compute ā xb. 3. Find a vector that is orthogonal to the…

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Q: -dx 23+1

A: Given :

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: 2. Determine the area of the region bounded by the curve y = x3 – x2 – 2x, and а. the x-axis

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Q: Solve the differential equation Bernoulli Equations: (x² + y²)dx – xydy = 0

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

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Q: the area of the region. 4 y = y 5- 2 1 5 10 3.

A: Topic:- application of integration

Q: Evaluate each integral. dr 1. VI² – 1 2. [zcos I Cos az dz 7x +1 dr 2-- 2 3. 7 – I – z

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Q: am confused can you highlight answers please thank u

A: From the original solution the answers are: Intercept: 0, 0 Relative minimum: -5, -110 Relative…

Q: Describe the applied transformations from y = 32 to %3D graph the function g(x) = -2(3)-2x-6 + 9 %3D

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Q: Write the binomial expansion for the following expression. (1*+1) 5 (1* +1)° = (Simplify your…

A: To write the binomial expansion.

Q: 5 3. (1 – x²)ždx

A: To evaluate: I=∫01(1-x2)52dx

Q: Find div F and curl F if F(r, y, z) = 2e*"i– 9cos yj+ 4 sin² z k. div F= curl F=

A: Given: F(x,y,z)=2exyi-9cosyj+4sin2zk

Q: Evaluate the integral dx (5x + 9)* by making the appropriate substitution: u = dx (5x + 9)*

A:

Q: Determine if i = (1,0.-4) and w=(9,3,1) are parallel vectors.

A: Use the vector product to show the given vectors are parallel.

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: 6. lim (sinx)*

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Q: Find the limit. NOTE: Enter the answer using round brackets. t? +9 1 lim t+oo 3t2 + 4' 6t = (?, ?)

A: 1/infinity=0 is used

Q: Evaluate / (x- 16)dA where Ris the region in the first quadrant enclosed between y = xand y = x².…

A: ∬Rx-16dA where R is the region in the first quadrant enclosed between y=x and y=x3

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

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Q: 524–121x4 lim x00 62xº+24x4+234x³+11x2+169 ||

A:

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

A: Consider the indefinite integral

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: INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) lim = lim Еquation…

A: This question is based on L hospitals rule.

Q: Solve the differential equation Integrating Factor by Linear Equation: (xy² + x²)dy + xydx = 0 %3D

A:

Q: If f (x)= [a(«) =os* '(5) [1+ sin(t?)] dt find f 1 dt, where g(x) V1+t3 COS X

A: We need to find value of derivative.

Q: Use the function to find the image of v and the preimage of w. T(V1, V2) = (V1 + V2, V1 - V2), v =…

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Q: sinh(3 In(a)) = (A) - (B) a³ – (C) 을 + 3a - (D) – 11 -18 -13 - -

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Q: Find the Taylor series for f(x) centered at the given value of a. [Ass f(x) = In(x), a = 6 |(-1)*+1…

A: We can solve this as follows:

Q: the 6) Find the a by curves y=x° and y=X ea of the region enclosed A) D)

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Q: L. dr 16. (I + 2)² 1 dz 17. x(x+2) 18. / arctan Vr dr

A:

Q: Question 1 Find the centroid of the given region. y-2- A (8/23,76/111) B (5,15) (c (3/22,45/61)…

A: The expression for the centroid is: For the x coordinate of the centroid: x=1A∬xdydx  For the y…

Q: ) Sypposef and g are functionns with continu lerivatives, and that they satisty the followia…

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

Q: itいて)ttいz (Stu) ८(S+4च) uft-)$+ no C2n7s)22n?1 znt1)! u(tー) tつa 2nts iuZetuてと(ttat) て tuて ttuて ut-)…

A: maclaurin series