Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). %3D v (0, 24) %3D a = %3D

Q: Evaluate the following, 8 [? + 3) e-2* dx, and write your answer in the form g(x) e¯2x + C.

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Q: Find the extrema of the following function on the given interval, if there are any, and determine t...

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Q: Use Squeeze Theorem to evaluate -2x lim e COS x x 00

A: Based on the squeeze theorem or it is also been called sandwich theorem we can evaluate the limit by...

Q: Read Theorem 6.2 in the textbooke. Suppose that E cn an is a power series with interval of convergen...

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Q: Find the vector component of v = (4, – 1, 7) along b = (4, 8, –8) and the vector component of v orth...

A: I am attaching image so that you understand each and every step.

Q: A. Directions: Use the figure below in naming four pairs. 12 2 11 3 10 4 9 5 8 1. alternate interior...

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Q: 9. Let a be a positive value. State the integral test, and use this to determine whether ). -an e n=...

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Q: Let f be the function defined by f (æ) = Which of the following is the Maclaurin series for f'? %3D ...

A: The objective is to find the maclaurin series of  f'.

Q: Match each Power Series with it's centre. One of the series is not a Power Series, so match that ser...

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Q: 17. у %3D 5x + 1, у%3D6, х%3D0

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Q: Given the following System of Differential Equations and its Eigenvalues and Eigenvectors 1 2 has Ei...

A: From the given options  Option (B) closely define the differential equation for given system because...

Q: entiable at x = 1. What is f_(1)?

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Q: 9. given f(-2) = 5, f'(-2) = -3, g'(-2) = 6, f g)'(-2) = 15. Find g(-2) %3D

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Q: Let S 8x x 30 f(x) 70 Evalute f(x) dx.

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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: If the base b of a triangle is increasing at a rate of 3 inches per minute while its height is decre...

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Q: 1. Using Logarithmic Differentiation, find dy given that dx -3 sec-(VT) y = 4*(log2 r)sech z"

A: This is a problem related to differentiation of the function. Based on the logarithm property we wil...

Q: Given a point in cylindrical coordinate (4, , -4 ), find its equivalence in spherical coordinate. Dr...

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Q: Find the indefinite integral. (Use C for the constant of integration.) sin3 50 v cos 50 de

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: Let A = [0, 1] and define fn(0) = fn(;) = fn(1) = 0, fn(;) = n and fn to be linear on each of the se...

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Q: Find the slope of the graph of the function at the given point. 256 f(x) = (4, 1) f'(4) =

A: Explained below 

Q: Find the volume of the solid that is obtained by revolving the region about the line y = 2. %3D 个ッ 3...

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Q: Find the volume of the solid obtained by rotating the region bounded by y= 2 andy = = 2x about the l...

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Q: Approximate the critical numbers of the function shown in the graph. Determine whether the function ...

A: Solution ) 1) critical number are peak or valley points Here x = 2  Graph gains maximum value  criti...

Q: 16. t 31²y = cos t, y(T) = 0 dt

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Q: Find the standard (slope-intercept form) equation of the tangent line to the following functions at ...

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Q: Let a = ci +j and b 8i + 6j. Find c so that the angle between a and b is Round your answers to four ...

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Q: Consider the following planes. -5x + y + z = 5 15x - 3y + 5z = 25 (a) Find the angle between the two...

A: Let's find. 

Q: use mathematical induction to prove the formula for all integers n ≥ 1. 1+2+2^2+2^3+•••+2^n-1 = 2^n ...

A: Given the statement is "For all integers n≥1,  1+2+22+23+ ⋯ +2n-1 = 2n-1".

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 20j as ...

A: topic - vectors

Q: lume of a tetrahedron with adjac 1 w is Ju· (v x w)| to determine 6. tices P(-3,2,0), Q(2, 1, –3), R...

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Q: Determine the coordinate of the centroid bounded by curves of the polynomial functions y = #³ – z an...

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Q: How far from the x-axis is the centroid of the area bounded by the curve y = 8x, the y-axis and the ...

A: Solution is given below:

Q: Find the critical points of the function f(x,y)=x^2+y^2+6x−10y+1

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Q: Use the Product Rule or the Quotient Rule to find the derivative of the function. f(x) = (6x² + 9)(x...

A: Given,         F(x)=(6x2 + 9) ( x2 - 5x - 8)

Q: Find the volume of the solid generated by revolving the region bounded by the graphs the first quadr...

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Q: du 17. t = t² + 3u, t> 0, u(2) = 4 dt

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Q: Evaluate the limit: x2−9−/5x+15=   limx→3

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Q: y"-8y'+2y xe

A: Answer of given question is in step2

Q: Q22 coordinates of a point Sammy is given the cartesian (-1,-53), He lp Sammy find polar coor dinate...

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Q: 13) For the given cost function C(x)=48400+800x+x2C(x)=48400+800x+x2 find: a) The cost at the produc...

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any sp...

Q: find the differential dy if y= sqrt(2x^5-3x

A: Given query is to find the differential of the expression.

Q: 3. U sin g Derivative Product rule 3. (x + 6) (x + 5); 4. 4x² (x – 1)

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Q: .. Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not...

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Q: Find the centroid of the region bounded by y^2 =4ax, y=mx about y-axis.

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Q: Consider the differential equation dy = y +t. dt Given that the general solution to the DE is y(t) =...

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) (x) - 3x2...

A: For critical points, we take f'(x) =0

Q: 2. Fill in the blanks Let y be a solution of the differential equation y' = , where – 1 < x < 1, –1<...

A: ∫1a2-x2 dx = 12aln1+x1-x+C