Using Trigonometric Substitution a substitution of x = 6 sin(theta) was used to solve an integral. The resulting antiderivative is given: Fill in the given right triangle AND write the antiderivative in terms of x. Your final answer should contain NO trigonometric functions.

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Q: Iƒ F(t) =î+tj+t²k and G(t) = tî+e¹+3k, then find (F × G)(t) at t = 0. 0 Ok O î+ ĵ + k o î+î

A: Topic- Cross Product of vectors

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A: Please see the below picture for detailed solution.

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A: Given data:- Order value of fine paper = 1000 units Produced at two location, x1 & x2 The cost…

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A: As we know that; The Sum/Difference Rule: f±g'=f'±g' The Power Law: ddxxn=nxn-1 And a·f'=a·f', where…

Q: Question Find the linear approximation L(x) of the function f(x) = cos(x) at a = - 품. (Enter an…

A: We can find the linear approximation as below.

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A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: dy Solve the differential equation: = A - By. Find the general solution to the dx differential…

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Q: 21. If u = - y+z a) 0 Z z+x x+y b) 1 ди then the value of x + y + z 2 is: c) u d) None 22. The…

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Q: Q 14) Does the sequence converge or diverge. If it​ converges, find the limit.

A: Concept: Infinite series converges and diverges: Let ∑k=1∞ak be an infinite series, and let an be…

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A: Given query is to find the value of the integral.

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A: To find the missing limits of integration.

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A: Need to find out the solution and also the values of r

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A: Solution is given below:

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A: Given:    Gr=x+y+z,    S: z=2x-y       0≤y≤1, 0≤x≤y Substitute z=2x-y in Gr     Gr=x+y+2x-y…

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A: Formula to calculate :-Density=MassVolumeVolume of the cone=13πr2hwhere r=radius of the base of the…

Q: 8. Consider the differential equation e* (y - x) dx + (1 + e*) dy = 0. (a) Show that this is an…

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A: Given that,            The solid is obtained by rotating the region bounded by the given curves…

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Q: If the sequence { 2 9 - An An - 3 converges to 6, then the sequence {an} converges to 9.

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Q: Solve the differential equation y'=1+5y subject to the initial condition y(0)=1. From your solution,…

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Q: O O 2x4 1,34 dx +1 NIS In[x5 + 1] + € C In[x5 + 1] + C 5 In[x 5 + 1] + C In[x5 + 1] + C

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Q: Solve the initial value problem. ds dt I cost- sint, s = 3 2

A: To solve the initial value problem.

Q: 1. Calculate the following unknown quantities. (a) P= (kx 1000), r= 1.2%, t= Find S.

A: As per the rules we can answer only first question and rest can be reposted.

Q: 9 == find f'(x) using the limit definition of the derivative. x Given f(x) = f'(x)=

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