Ise Part 1 of the Fundamental Theorem of Calculus to find the derivative of the fum 8(x) = [" 1 dt t +1 7. g(x) = [ e"* %3D

Q: Find the area, A, of the region enclosed by the cardioid r = 8+8 cos 0.

A: Given   area can be given as below :

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: 13. 1²V2 - 1 dr

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

Q: Solve the differential equation Integrating Factor by Inspection: (2y – 3x)dx + xdy = 0

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Q: Evaluate the integral * (2* – 8)* dz, 33 by making the appropriate substitution: u = 33 NOTE: Your…

A: We need to evaluate the following integral I = ∫x3x4-833dx                         ..........1…

Q: 10 X=-3

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

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Q: 14) f' (x) =(sin 3 x)'=, A) – 3(cot2 x) csc2x C) 3(tan2 x) sec2x By Power Rule B) – 3 sin2 x cos x…

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Q: dx (x- 3)

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other questions as…

Q: 3. Find a unit vector that points in the opposite direction as = 27 +7]-5k. %3D 4 Find a vector that…

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Q: Find V · (V × F), if F(x, y, z) = e"i+ 3ze'j – 5e"k. V. (V × F) =

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Q: Find ag and a, for the following geometric sequence. 4 4 12, - 4, 3 9 a5 = (Simplify your answer.)…

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Q: Evaluate the integral by making the given substitution. (5x)tan(5x)dx, u = 5x + C

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Q: H.W (3) 1- find fxy fxx fyx fyy for f (x,y) = x2 +3xy- y*

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Q: Write an iterated integral for d. dA over the region R described to the right using R a. vertical…

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Q: 4 sin 3xcar" 3xdx

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Q: 7 Evaluate the sum i(3i + 2) i=1

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Q: 5 3. (1 – x²)ždx

A: To evaluate: I=∫01(1-x2)52dx

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

A: To evaluate the given limit of the function.

Q: 4. The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the…

A: Given: Let the three digit number be  'xyz'  where x is 100th digit, y is 10th digit and z is units…

Q: Use double integration to find the volume of the solid bounded by the cylinder x² + y? = 16 and the…

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Q: Follow the instructions. Typewritten for upvote.

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Q: -2 12) Find the sum of the Series 2".30" A C) D) 2 E) 9

A: Let    I= ∑n=1∞2n3-n-2Rewriting 2n3-n-2=2n3-n3-2                                  =2n3n×132…

Q: Evaluate the triple integral. Xyz dV, where G is the solid in the first octant that is bounded by…

A: Integral

Q: x²+x dx x2+1

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Q: Find T(t) and N(t) at the given poi: x = e cos t, y=e' sin t, z = %3D %3D T(0) = N(0) = %3D

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Q: y" + 2y' + 5y = 3 sin(2t)

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Q: =/2 4. cos z dr Jo da 5. I+1 I +IA

A: We have to evaluate the indefinite integral

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: A business is planning to purchase a piece of equipment that will produce a continuous stream of…

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Q: Follow the instructions. Typewritten for upvote. No upvote for handwritten. Thank you

A: We have to find the number

Q: Evaluate the indefinite integral. (Use Cc for the constant of integration.) |

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Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

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

A: Volume

Q: 1. Find the area enclosed by the given curve, the x-axis, and the given ordinates (a) The curve y =…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 +8 1 lim t+oo\ 5t2 + 6' 8t (?, ?)…

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Q: 47. f(x) = V(3 – x) on [1,3]

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Q: farctan(6y) dy: Consider the integral 1+ 36y2 This can be transformed into a basic integral by…

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Q: For problems 1- 2determine the dot product, a-b. 1. ā = 9ĩ -8k , 5 = (3.-2.1) 2. and the angle…

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Q: -2x (1+ee) dx e

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Q: Let the functions 13:R-¬R, with 3 メー X2 Proove that. V(4xs) =3 (Vx{)-4 (Vx)

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Q: 3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1…

A: Given problem:-  A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

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: 1. 15 dx (x-)2

A: Given problem:-

Q: 13. r²/2 – 1 dx

A: As per our guidelines, we can help you in solving only first problem , rest of the problems you have…

Q: Perform the following integration. If a u-substitution is needed, indicate the choice for u. -dx…

A: using method of substitution

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

A: Given: y=lncschx+cothx

Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

A: This question can be solved using the concept of area under curve.

Q: 22. (x+1)v2r-1 dr

A: Note: According to our expert guidelines only one individual question is to be answered kindly…

Q: I. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) f'(x) lim = lim Equation 1…

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