If a given function is an even function, then prove that f(x)dx = 2 f, f(x. Graphically support your answer. %3D

Q: (b) Sketch the vector with its initial point at the origin. sider the following graph. (4, 4) (4, 4)...

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Q: 4. (3x – y)2 = 6x + 2y + 23 @ (1,-2) 5. x(x² – y²) = 3 @ (-1,2)

A: 4) (3x-y)2=6x+2y+23, @(1,-2) 5)x(x2-y2)=3, @(-1,2).

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Q: If we want to evaluate the integral x+18 1= +64 dx, and dx = do and therefore the integral becomes, ...

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Q: Find u v, u· u, ||v||2, (u · v)v, and u · (3v). = (2, 11), v = (-5, 2) %D (a) A. n (b) u u (c) ||v||...

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Q: Find the interval of convergence of the series k(x+ 2)* 5k+1 k=1

A: The given series is: ∑k=1∞k(x+2)k5k+1...(1) Let, ak=k(x+2)k5k+1; k≥1

Q: Find an equation of the tangent line to the curve at the given point. y = In(x2 - 8x + 1), (8, 0) y ...

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Q: d sets of parametric equations and symmetric equations of the line that passes through the given poi...

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Q: onsider the following planes. 3x + 6y – z = 84 X - 12y + 2z = 0 (a) Find the angle between the two p...

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Q: Consider the following. u = (5, 9), v = (2, 4) (a) Find the projection of u onto v. 38 38 5' 10 (b) ...

A: We have to solve given Questions.

Q: Next que Does the sequence (a,) converge or diverge? Find the limit if the sequence is convergent. a...

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Q: Does the sequence {a,} converge or diverge? Find the limit if the sequence is convergent. In (n + 6)...

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Q: 6. Find the centroid of each of the given plane region bounded by the following curves: y? = x³, y =...

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Q: , evaluate the given double integral. I sinxcos(y – n)dxdy 10.

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Q: Question 8 In(t2 + e2)- 2 lim t 0 (a) 0 (b) 1 (c) 1/2 (d) 2 (e) none of these Question 9 The slope o...

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Q: 2 - Find: (a) 3a ,(b) a +b , (c) a-b , (d) la + b|, (e) a- b|, (f) 3a – 4b and (g) | 5a + 2b|. If 1....

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Q: Find the function s(t) satisfying = -2-3 cost dt and s(0) = 6. ds = -2-3 cos t dt and s(0) = 6 is s(...

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Q: Cx) = *-2r+2 a-1 c = 2

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Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3), P2(5,...

A: We can solve the given problem as follows:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

A: The equation of the plane P which is normal to the vector n and passes through the point R is given ...

Q: Find the volume of the torus (donut) with radii r and R as shown in the figure.

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does...

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Q: 3The bell tower of the cathedral in Pisa, Italy, leans 5.6 from the vertical A tourist stands 105 me...

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Q: Use the definitions of the hyperbolic functions to find each of the following limits. (If the limit ...

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Q: Find the angle 0 between the vectors in radians and in degrees. u = (2, 2), v = (4, -4) %3D | (a) ra...

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Q: explain to me details what is Distinguish Between Partial Derivative and Ordinary Derivative ?

A: Given

Q: Determine the equation of a tangent to the curve: y =. (x3 - 5x + 4)(3x2 - 2x) at the point (1,-2)

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z? = 21, (1, ...

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Q: Consider the following differential equation - (8 – r) dr + 9rds = 0

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with ...

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Q: if cosh(x)=41/40 and x > 0, find the other hyperbolic functions of x

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Q: Find the point of tangency and equation of the tangent line of the following functions given a singl...

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with ...

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Q: Consider the following. 5i + 6j, v = 7i + 9j U = (a) Find the projection of u onto v. (b) Find the v...

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Q: An aquarium 7 m long, 3 m wide, and 4 m deep is full of water. Find the following: the hydrostatic p...

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Q: Question 6 The area of a square is increasing at a constant rate of 1 cm2/sec. How fast is the diago...

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Q: | (r – 1)³ + 1, if x 2 1. Determine if g(x) = is differentiable at x = 2.

A: Checking continuity:=limx→2- g(x)=limx→2- (x-1)3+1  limx→2- g(x) =2Right hand side limit=limx→2+ g(x...

Q: 00 5 Write out the first few terms of the series > (- 1)" ) What is the series' sum? n = 0 5n ... Th...

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Q: The vector v and its initial point are given. Find the terminal point. v = (4, -9); Initial point: (...

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Q: Find the centroid of each of the given plane region bounded by the following curves: y = x³,y = 4x [...

A: follow the procedure given below.

Q: If using Trial and Error to factor ax^2+bx+c, a not equal to one, explain the procedure to use if b ...

A: Given quadratic polynomial :  ax^2+bx+c               ,where a ≠1   Aim: Explain the procedure of us...

Q: Consider the following. u = (8, 7, 2), v = (-4, 1, -9) (a) Find the projection of u onto v. (b) Find...

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Q: In the given first-order differential equation below, xy – 2y= x2In(x), y(1) = 5 (i) Identify the ty...

A: Given a differential equation.  

Q: Find u v, u· u, ||v||2, (u · v)v, and u · (3v). = (2, 11), v = (-5, 2) %D (a) A. n (b) u u (c) ||v||...

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Q: ) The natural length of a spring is 8 inches. A force of 20 lb stretches the spring to 10 in. Find t...

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Q: Find u · v, u · u, ||v||2, (u · v)v, and u · (3v). u3 (2, 11), v = (-5, 2) %3D (a) A.n (b) n.n (c) |...

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer ...

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Q: If f(x) = 8x* arctan(3x*), find f' (x). f' (æ) =

A: Answer is given below.

Q: Simplify the equation j4321 + j8765 + j6789 - j4000 O 1- 3j O 3-j O j^3 - 1 O 3j - 1

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Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it o...

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