Calculate the area of the region bounded by the graphs of the given equations. x 2y2- 4, x = y2 + 5 O A) 27 O B) O C) -12 D) 36

Q: A _1. (2x – 3) dx A. -2 _2. L(x3 + 2x) dx В. 0 _3. (x² – 2) dx 1 С. 3 4. S(x3 + 3x – 1) dx 2 D. 2 |…

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Q: Solve for x. log x = - 4 0.0001 -0.0001 1.386 -4

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Q: Find the average value of the function f(x,y)=eˆ(y/x) over the region bounded by y=x, the x-axis and…

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Q: 2ln|x| + 3 ln|x + 1| – * - + C 5x2+11x+2 dx x(x+1)2 2ln|x| + 3 In|x + 1| ++C 4 2ln|x| + 3 ln|x + 1|…

A: Given: I=∫5x2+11x+2xx+12dx   As we know that; The Power rule; ∫ax+bndx=ax+bn+1an+1+C And…

Q: Evaluate the iterated integral: x + 4y dx dy Answer :

A: We can solve as follows

Q: Solve [D* +3D² –4]y= 2sin° (5x)

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Q: dx 1-e-* Evaluate A. 2ln|e* – 1|+ c B. Inle* – 1|+x +c C. 2 In|e* – 1| +x+c D. Inle* – 1|+ c

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Q: 8. Relationship Between Continuity and Differentiability: (a) Justification needed): If lim…

A: To discuss the  relationship between continuity and differentiability.

Q: Compute each sum below. If applicable, write your answer as a fraction. 4 + ...+ 4(3)- 0 + 4(3) +…

A: Use geometric series sum concept

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. e2x –…

A: Solve the exponential equation algebraically.

Q: ||r(t) × r"(t)|| ||r'(t)||* Use the formula k(t) : to find k(t). r(t) = e"i+ ej K(t) :

A:

Q: 2. A rocket is launched in the air. Its height (in meters above sea level) as a function of time t…

A: To solve the following problem

Q: The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term and the…

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Q: Solve the equation algebraically. Round the result to three decimal places. 3+ln x = 0 8 e-354.598…

A: Using algebra

Q: :. Let x(t) = 2 sinh t , y(t) = cosh(t²) be a curve in the Oxy-plane, given in parametric form. (a)…

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Q: Evaluate (z° + 6) dæ (z³+6)® +c А. 18 (z³+6)° В. +c (x³+6)* 16 С. z18 + 2x15 + c

A: topic - indefinite integral

Q: testconuer gnce and diverg ence 2+5 3"

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Q: Find the (2x + 1)³ dx A. (2x + 1)2 +c (2x + 1)3 + c 8 С. (2x + 1)4 + c D. (2x + 1)* + c 4 B.

A: We have to find the indefinite integral of given function

Q: is an angle in standard position, tan(e) 0, then the terminal side of lies in which quadrant? A IV…

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Q: Find V · (F × G), if F(x,y, z) = 3xi+j+7yk and G(x, y, z) = xi+ yj – zk. V• (F × G) =

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Q: The graphs of the function f (r) = 7 - a and g(a) = 3 are given below. %3D

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Q: In sketching the graph of y=f(x) = – 3cos +)+4, we translate the graph of y = - 3cos s 5 by 4 units…

A: Transformation of graph

Q: Given h(r) = 1/r+3 find the following: (a)h(x2)= (b) h(x2 + 1)= (c)h(x2) + 1=

A:

Q: Find these derivatives

A: Our Aim is to find the derivative of the following functions given below:-(i) y=e2x cos (x)(ii) y=ln…

Q: Find the Inverse Laplace Transform of the following functions: 16 a. L4. s(s2-14) b. L4. (25-32)2

A: we have to find       L-1{16s(s2-14)}   we can re-write the function 16s(s2-14) =1614( -1s +ss2-14 )…

Q: Given that f'(x) is continuous everywhere and changes from negative to positive at x=a, which of the…

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Q: Change the order of integration. f(x, y) dy dx Jo

A: 0≤x≤10≤y≤xRegion bounded by:x=0, x=1y=0, y=x

Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5

A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2  ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2

Q: dx 00 2 X х +4

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Q: Area A = 1,427 Calculate the definite integral f(x) dx by referring to the Area B = 2,460 Area C =…

A: Here we will find the definite integral,

Q: Clear denominators in the following partial fraction decomposition and determine the constant B. 3x?…

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Q: Find V × (V × F) if F(x, y, z) = 9xyj+2xyz k. V x (V × F)

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Q: ||r(t) × r"(t)|| Use the formula k(t) : to find «(t). %3D r(t) = e"i+e-tj K(t):

A: K(t)=?

Q: 3. Draw an example where ja + D|

A:

Q: Let ABCDEF is a regular hexagon with centre O. Let ā = 0A, b= OB and so on. Explain why/prove %3D…

A: We know that in an regular hexagon the distance from center to any vertex is same, then the…

Q: 2. Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

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Q: The velocity of a car is v(t) = 42(t - 2)(t - 4) miles per hour on the time interval [0, 4] hours.…

A: We need to find distance traveled by car.

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

A: Here we have to find the volume.

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

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Q: For the curve given by r(t) = (5 sin(t), –2t, – 5 cos(t)), Find the unit tangent T(t) = (| Find the…

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Q: 2x x– 3)² A = 6, B = 2 A = 2, B = 6 A= 2, B=-6 A=-2, B -6 A= -2,B 6 None of the Above Other:

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

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Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

Q: a) fx² sec2

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Q: Find ▽ x (▽xF) if F(x, y, z)=10xy j+ 10ryz k.

A: The value of ▽ x (▽xF) is (10 + 10y)i + 10xj + 0k

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: 7. Consider the function f graphed below. 2 -4 4 -2

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Q: -(1/3), 3/9, -5/27, 7/81

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Q: d d Calculate r1(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: 6 + (-3) + 0 + ..+ 411 = 97 (a* + 5) - 0 k = 1

A: