Find the area of the region enclosed by the curves y=x2−1 and y=8.

Q: Consider the integral cot(0) · In(6 sin(@)) d0: This can be transformed into a basic integral by…

A: We have to find the integral.

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: Question 8 Find the volume of the shaded region when revolved about the indicated axis. 21 x = V7+y…

A: Application of integration

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: -Find Taylor or Maclaurin for the following functions: 3) 2) f (x) = e* at a = 2

A: A detailed solution is given below.

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

A: Let, First number = x & 2nd number = y therefore, x+y=25   & x-y= 7

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A:

Q: 7. Find the area of the region bounded by y = 5x² +1, x = 0, x = 2,y = 0. Give a sketch of the…

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Q: 5. The denominator of a fraction is four less than the numerator. If the denominator is doubled and…

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Q: 10 X=-3

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Q: 1.) ° 6x3+4x²-8x dx I. Evaluate the following Definite Integral. 1.) ° 6x³+4x²-8x 2.) x²(2x3 + 1)Fdx…

A: we want to find the integral ∫03( 3x-6 -1 )  dx

Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: II. Find the Inverse Laplace of the following 2s-9 d. s2 +2 1 е. (s²+1)(s²+4s+8)

A:

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

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Q: 5.) Find the volume generated by revolving the area bounded by the curve y2=4x, x = 0 about the line…

A: Given area is bounded by: y2=4x and x=0. The area is revolving around the line y=4. From y2=4x we…

Q: dx

A: A detailed solution is given below.

Q: D) 2/0- D)-2y/C 9) Given a piecewise function below f(x) = (1- x)*n (x>0) , Find lim f(x) =r hpli te…

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Q: Find the particular solution of the DE y''-11y'+24y=0 when y(0)=2 y'(0)=-3

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Q: Solve for all values of x. 1, 12x+9 6-322+9 36 Answer: Submit Answ

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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

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A:

Q: Calculate ri(t) · r2(t)] and r.(t) × r2(t)] first by differentiating dt the product directly and…

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A:

Q: Solve the problem. A conitant force F 10+ 30J. moves an object from the point P= (6, 4) to the point…

A: Given  F=16i+30j             P=(6,4) & Q=(3,18) To find work-done:

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Q: Solve the following differential equations of dy 1 -·y = xy'; dx

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Q: Question 2 of 4 (x² – 1)(x + 1) (x2 – 2x + 1) :- f (x) =

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Q: -dx 23+1

A: Given :

Q: Question 16 Find the equation of the tangent plane to the given surface at the indicated point. x2…

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Q: Obtain the limits of the following functions: (2sinx-sin2x 1. lim x-sinx

A: To evaluate the limit of the function.

Q: Find V (V x F), if F(z, y, =) = 3e""i+7ze'j – 3e"k. V. (V x F) =

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Q: 3 Evaluate the integral c Ħ A) 1 B) 77 c) - Ť tan?xdx E)ユ-

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Q: Suppose that f (x) is a function such that lim f(r) and lim f (r) both exist. Does this mean lim…

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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: Question 7 Use cylindrical shells to find the volume of the solid generated when the region enclosed…

A:

Q: Find the indefinite integral. (Use c for the constant of integrat (4t3i + 4tj – 6vik) dt

A: we use the basic formula ∫xn dx =xn+1n+1+C    ; n≠-1

Q: Consider the indefinite integral le*+3 dx: a) This can be transformed into a basic integral by…

A: Explanation of the answer is as follows

Q: 1.) Find the area bounded by the curve y?= 1 - x and 2y = x + 2 2.) Find the area bounded by the…

A: Solution is given below:

Q: Qg Solve: coshx-1 .dx

A: Basic hyperbolic identities are used along with integration identities.

Q: The eccentricities and foci of a hyperbola centered at the origin of the xy-plane are shown below.…

A: The eccentricity of the hyperbola centered at the origin of the xy-plane, e = 2 The coordinates of…

Q: 6. lim (sinx)*

A: u =eln u, then:limx→0+  (sin x)x  =limx→0+  ex ln(sinx)=limx→0+  eln(sinx)1x=elimx→0+  ln sin(x)1x

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Q: 1. Given ā = 31 -9j and 5 =-6i +j compute each of the following. (a) 105 (b) 14ã + 205 (c) 85- 2.…

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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: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D %3D a. Write the unit vector for s- b.…

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Q: Use a triple integral to find the volume of the solid shown in the figure. z = 16 – x2 - y2 130 10…

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Q: e* dx V1-e2x

A: Topic = Integration

Q: Simply the integral dx using am X²+4 A a ate trigonometric substitution. S sin edo DS sec edo dS1de…

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Q: 26) In Problem 26 and 27, given f(x)dx= - 1 J g(x)dx= 2 and S f(x)dx= 3 a a d. Find f" f(x)dx + S*…

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Q: Find the vector projy u. u = 3 i - j+ 3 k, V = 2 i+ j+ 2 k

A: We want to have projection vector. Projection of vector u on v is given by u.vvv⏞