(-1)" 2'/n (2n² – 1)" en? n=1

Q: 1. Simplify. a. 2168 3i-89 + 4i114 125 +21213 31-314 b. 597 4185

A: a.Solution :2i68-3i-89+4i114we know that i2=-1i3=-ii4=12i17×4-3i-22×4+1+4i28×4+22i17×4-3i22×4+1+4i28...

Q: х? + ах — 2bx — 2ab — х3 —2ax* — 2bx? dx х4 + ах3 — 2bx3 — 2abx? |

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Q: V9-4x? - dx

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Q: 11. A gate in an irrigation canal is constructed in the form of a trapezoid 3 ft wide at the bottom,...

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Q: Question 8 x2dx Evaluate | x2Vx2-4

A: Solution

Q: 12 Find the area under the curve y = over the interval [ – 1, 1]. (x + 2)² area = i

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Q: /2 Evaluate using Wallis' Formula: sin5 x cos6 x dx

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Q: Evaluate using Wallis' Formula: 7 sin? x cos5 x dx

A: follow next step

Q: (2 cos x–sin x )" dæ sin x

A: Given: I=∫2cosx-sinx2sinxdx   We know that; The trigonometric identities; 1). sin2x+cos2x=1 2). 1csc...

Q: Sy? sin y dy

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Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (x – 2)2 = 4(y + 2) ...

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Q: A. Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector...

A: To find out the unit normal vector to the surface at the given point.

Q: Let a = ci + jand b = 8i + 15j. Find c so that the angle between a and b is. Round your answers to f...

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Q: Find S z? sin z dz

A: We will solve this question, using integration by parts .

Q: dx -2 3 (5-4x- х?)2

A: Let's find. 

Q: How-3 Find Zxx if Z=fcusvd uz x?y,V=2xy Exfress the answer interms of Xy, Zu, Zv

A: Implicit Differentiation: If z=f(u,v) , u=g(x,y) and v=h(x,y) then, ∂z∂x=∂z∂u∂u∂x+∂z∂v∂v∂xand ∂z∂y=∂...

Q: Znt 2

A: For the series with an=(-1)n+1 bn  or an=(-1)n bnbn ≥0 for all k.Then if,1. limn→∞ bn =0 and,2.{bn} ...

Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j. NOTE: Enter the exact answe...

A: The unit vector in the direction of u is defined by: {\displaystyle \mathbf {\hat {u}} ={\frac {\ma...

Q: 2 2 cos 0 d0 V1 – sin 0

A: Given:        ∫0π2cosθ1-sinθdθ substitute u=1-sinθ→dudθ=-cosθ→dθ=-1cosθdθ      =∫10-1udu       =-∫01...

Q: 3 dx o v9 – x²

A: We know that,  ∫dxa2-x2=sin-1xa+C ∫03dx9-x2=∫03dx32-x2                    =sin-1x3+C Now applying th...

Q: Evaluate (*(x-2) (х-1)3

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Q: Find the volume of the solid generated of the area in the first quadrant bounded by y = 3x

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Q: dx Evaluate x²V4+x²

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Th...

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Q: 12. f (x) = x³ – 2x² + x – 1 ; (-4,5)

A: Function is called as an continuous if its right hand side and left hand side limit is equal.

Q: g(y) = y3 dy y 4 3+ 1 4 6. 8

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Q: In Exercises 39-42, the velocity v(t) of a particle moving in the plane is given, along with the pos...

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Q: Let a = ci + jand b = 6i + 54j. Find c so that a and b are orthogonal. C = i

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A: Given equations are:  x2+y2-2ax=0x+y=2a

Q: Let D be the smaller cap cut from a solid ball of radius 20 units by a plane 10 units from the cente...

A: Given sphere:  x2 + y2+z2 = 202                     sphere

Q: Evaluate f 1+cos 4x dx 1-cos 4x

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Q: onsider the points A(3, -3,3), B(4, –5, 1), C(-2, –-4, 1), and (6, 3, -5). -) Find the volume of the...

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Q: What is the slope of the tangent line to the graph of y = x3 – 4x + 2 at point (2, 2)? %3D А. 1 В. 4...

A: Given function, y=x3-4x+2Diferentiate w.r.t. xdydx=ddx(x3-4x+2)dydx=3x2-4dydx(x,y)=(2,2)=3(2)2-4dydx...

Q: Estimate the area under the graph of f(x) = x² + 3x + 1 over the interval [2, 4] using ten approxima...

A: Given function: fx=x2+3x+1 Interval: [2, 4]Number of rectangles = 10 To find: The area under the gra...

Q: 3x 3. lim х-0 sinx

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Q: Find the length of the arc of the curve 9y? 4x3 from the origin to the point (3,2v3).

A: Here, the given curve is: 9y2=4x3⇒y2=4x39⇒y=23x32 Now, the length of the curve on [a,b] is given by:...

Q: ITxy* dy dx x2

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Q: A Find 32 31¥ and 22f fer the functions tre etan (x+y) 2- 우Cx,y) x ty + cosy +y sinx. %3D

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Q: Suppose a function z=f(x,y) has critical points at (-1,2) and (0,3). Furthermore, suppose at each cr...

A: Let's find. 

Q: 2 cos e de 2 V1 – sin 0

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (4,). %3D

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Q: f) {1,0,–1,1,0, –1,1,0,...}

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Q: Find the volume of the solid generated of the area in the first quadrant bounded by y = 3x – x3, x =...

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Q: 15. A tank contains 750 L of pure water. Brine that contains .12 kg of salt per liter of water enter...

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Q: x= y? – 4y (-3, 3) x = 2y – y²

A: Solve

Q: 13. Find an equation of the curve that passes through the point (1, 1) and whose slope at any point ...

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Q: Average Rates of Change Use each graph to estimate the average rate of change of the percentage of n...

A: We need to find the average rate of change for the given graphs.  

Q: x'y' = 4x? + 7xy + 2y? %3D

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Q: Evaluate f x Vx + 10 dx

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