(a) The vector in 2-space of length 7 pointing up at an angle of 2π/3 measured from the positive x-axis. j = sqrt(3) (b) The vector w in 3-space of length 5 lying in the yz-plane pointing upward at an angle of 5/6 measured from the positive y-axis. V k

Q: 1. f de 1-cos 8

A: Since you have posted multiple question in this question and i can solve first question as per our…

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A: The answer is given below

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A: I have stated the used formulas in the solution

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A: L'Hopital's rule is used. Chain rule is used to find the derivative.

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A: Given S=221775851217 and M=954310605648

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A: Given, ∫16-x2dx

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A: Given: The given function is fx=15x+4 To find: we have to find the value of f'5 Note: Multiple…

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A: Since you have posted multiple question in this question which are not interlinked so i have solved…

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A: To find the solution of differential equation

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A: find the function g(x) value at indicated x value.

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A: Given, limx→ 03x-sinxxLetL=limx→ 03x-sinxxL=limx→ 03xx-sinxxL=limx→ 03-sinxxTake separate…

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A: To Find: the component form of vector with magnitude and angle

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A: Ans=1/3 For detail...go through the solution ....I have solved in detail

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A: Given differential equation, y'=(2x-5)/2y So, 2ydy=(2x-5)dx

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A: Since multiple questions are asked, I am answering first question

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A: see below the answer and explanation

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A: As we know that; The standard form of the first order linear differential equation is: dydx+Pxy=Qx…